MathsGee Open Question and Answer Bank - Recent questions tagged grade12
https://mathsgee.com/qna/tag/grade12
Powered by Question2AnswerWhere can I get self study guides for Grade10, Grade 11 and Grade 12?
https://mathsgee.com/qna/10703/where-can-i-get-self-study-guides-for-grade10-grade-11-and-grade-12
Where can I get self study guides for Grade10, Grade 11 and Grade 12?DBE COVID QnAhttps://mathsgee.com/qna/10703/where-can-i-get-self-study-guides-for-grade10-grade-11-and-grade-12Fri, 15 May 2020 15:23:06 +0000Given the sequence $−15;−11;−7;…173$. Is this an arithmetic sequence? What is the formula of the general term?
https://mathsgee.com/qna/9621/given-the-sequence-15-11-7-173-is-this-an-arithmetic-sequence-what-is-the-formula-of-the-general-term
Given the sequence $−15;−11;−7;…173$. Is this an arithmetic sequence? What is the formula of the general term?Grade 12 Mathshttps://mathsgee.com/qna/9621/given-the-sequence-15-11-7-173-is-this-an-arithmetic-sequence-what-is-the-formula-of-the-general-termThu, 30 Apr 2020 07:21:16 +0000A quadratic sequence has a second term equal to 1, a third term equal to −6 and a fourth term equal to −14. Determine the second difference for this sequence. Hence, or otherwise, calculate the first term of the pattern.
https://mathsgee.com/qna/9615/a-quadratic-sequence-has-a-second-term-equal-to-1-a-third-term-equal-to-6-and-a-fourth-term-equal-to-14-determine-the-second-difference-for-this-sequence-hence-or-otherwise-calculate-the-first-term-of-the-pattern
A quadratic sequence has a second term equal to 1, a third term equal to −6 and a fourth term equal to −14. Determine the second difference for this sequence. Hence, or otherwise, calculate the first term of the pattern.Grade 12 Mathshttps://mathsgee.com/qna/9615/a-quadratic-sequence-has-a-second-term-equal-to-1-a-third-term-equal-to-6-and-a-fourth-term-equal-to-14-determine-the-second-difference-for-this-sequence-hence-or-otherwise-calculate-the-first-term-of-the-patternThu, 30 Apr 2020 07:13:25 +0000I cant see how common-difference and common ratio are not the same in sequences, can you help me understand?
https://mathsgee.com/qna/9614/i-cant-see-how-common-difference-and-common-ratio-are-not-the-same-in-sequences-can-you-help-me-understand
I cant see how common-difference and common ratio are not the same in sequences, can you help me understand?Grade 12 Mathshttps://mathsgee.com/qna/9614/i-cant-see-how-common-difference-and-common-ratio-are-not-the-same-in-sequences-can-you-help-me-understandThu, 30 Apr 2020 07:12:42 +0000Determine the general formula for the n term of each of the following geometric sequences: $5;10;20;…$
https://mathsgee.com/qna/9613/determine-the-general-formula-for-the-n-term-of-each-of-the-following-geometric-sequences-5-10-20
Determine the general formula for the n term of each of the following geometric sequences: $5;10;20;…$Grade 12 Mathshttps://mathsgee.com/qna/9613/determine-the-general-formula-for-the-n-term-of-each-of-the-following-geometric-sequences-5-10-20Thu, 30 Apr 2020 07:11:37 +0000Consider the following terms: $(k−4);(k+1);m;5k$ The first three terms form an arithmetic sequence and the last three terms form a geometric sequence. Determine the values of k and m if both are positive integers. [IEB, Nov 2006]
https://mathsgee.com/qna/9611/consider-the-following-terms-k4-k-1-m-5k-the-first-three-terms-form-an-arithmetic-sequence-and-the-last-three-terms-form-a-geometric-sequence-determine-the-values-of-k-and-m-if-both-are-positive-integers-ieb-nov-2006
Consider the following terms: $(k−4);(k+1);m;5k$ The first three terms form an arithmetic sequence and the last three terms form a geometric sequence. Determine the values of k and m if both are positive integers. [IEB, Nov 2006]Grade 12 Mathshttps://mathsgee.com/qna/9611/consider-the-following-terms-k4-k-1-m-5k-the-first-three-terms-form-an-arithmetic-sequence-and-the-last-three-terms-form-a-geometric-sequence-determine-the-values-of-k-and-m-if-both-are-positive-integers-ieb-nov-2006Thu, 30 Apr 2020 07:09:11 +0000$5;x;y$ is an arithmetic sequence and $x;y;81$ is a geometric sequence. All terms in the sequences are integers. Calculate the values of $x$ and $y$.
https://mathsgee.com/qna/9609/5-x-y-is-an-arithmetic-sequence-and-x-y-81-is-a-geometric-sequence-all-terms-in-the-sequences-are-integers-calculate-the-values-of-x-and-y
$5;x;y$ is an arithmetic sequence and $x;y;81$ is a geometric sequence. All terms in the sequences are integers. Calculate the values of $x$ and $y$.Grade 12 Mathshttps://mathsgee.com/qna/9609/5-x-y-is-an-arithmetic-sequence-and-x-y-81-is-a-geometric-sequence-all-terms-in-the-sequences-are-integers-calculate-the-values-of-x-and-yThu, 30 Apr 2020 07:01:00 +0000How many laws of logarithms are there?
https://mathsgee.com/qna/9593/how-many-laws-of-logarithms-are-there
How many laws of logarithms are there?Grade 12 Mathshttps://mathsgee.com/qna/9593/how-many-laws-of-logarithms-are-thereThu, 30 Apr 2020 06:09:58 +0000Given $T_{n} = 3^{n+1}$ . Which term is the first to exceed 20 000?
https://mathsgee.com/qna/1984/given-t-n-3-n-1-which-term-is-the-first-to-exceed-20-000
Given $T_{n} = 3^{n+1}$ . Which term is the first to exceed 20 000?Grade 12 Mathshttps://mathsgee.com/qna/1984/given-t-n-3-n-1-which-term-is-the-first-to-exceed-20-000Fri, 09 Aug 2019 02:58:24 +0000Given the series: 2(5)5 + 2(5)4 + 2(5)3 + ... Show that this series converges.
https://mathsgee.com/qna/1981/given-the-series-2-5-5-2-5-4-2-5-3-show-that-this-series-converges
Given the series: 2(5)5 + 2(5)4 + 2(5)3 + ... Show that this series converges.Grade 12 Questionshttps://mathsgee.com/qna/1981/given-the-series-2-5-5-2-5-4-2-5-3-show-that-this-series-convergesFri, 09 Aug 2019 02:55:16 +0000The sum of the first n terms of a sequence is given by: $S_{n}= n(23 - 3n)$
https://mathsgee.com/qna/1979/the-sum-of-the-first-n-terms-of-a-sequence-is-given-by-s-n-n-23-3n
The sum of the first n terms of a sequence is given by: $S_{n}= n(23 - 3n)$. Calculate the 15th term of the sequence.Grade 12 Questionshttps://mathsgee.com/qna/1979/the-sum-of-the-first-n-terms-of-a-sequence-is-given-by-s-n-n-23-3nFri, 09 Aug 2019 02:52:15 +0000Simplify $(e^(2 * ln(x)))$
https://mathsgee.com/qna/1295/simplify-e-2-ln-x
Simplify $(e^(2 * ln(x)))$Grade 12 Mathshttps://mathsgee.com/qna/1295/simplify-e-2-ln-xMon, 03 Jun 2019 04:50:45 +0000Express $((sin(x)^2) + (cos(x)^2))$ without using any trigonometric functions.
https://mathsgee.com/qna/1294/express-sin-x-2-cos-x-2-without-using-any-trigonometric-functions
Express $((sin(x)^2) + (cos(x)^2))$ without using any trigonometric functions.Grade 12 Mathshttps://mathsgee.com/qna/1294/express-sin-x-2-cos-x-2-without-using-any-trigonometric-functionsMon, 03 Jun 2019 04:49:57 +0000If $\log 5 = 0,7$, determine $\log_2 5$ without using a calculator
https://mathsgee.com/qna/1193/if-log-5-0-7-determine-log2-5-without-using-a-calculator
If $\log 5 = 0,7$, determine $\log_2 5$ without using a calculatorGrade 12 Mathshttps://mathsgee.com/qna/1193/if-log-5-0-7-determine-log2-5-without-using-a-calculatorFri, 24 May 2019 01:15:26 +0000Evaluate without using a calculator: $(\log_{ 7} 49)^5 + \log_{ 5} \: \biggl(\dfrac{1}{125}\biggr) - 13\:\log_{ 9} 1$
https://mathsgee.com/qna/1192/evaluate-without-using-a-calculator-log-7-49-5-log-5-biggl-dfrac-1-125-biggr-13-log-9-1
Evaluate without using a calculator: $(\log_{ 7} 49)^5 + \log_{ 5} \: \biggl(\dfrac{1}{125}\biggr) - 13\:\log_{ 9} 1$Grade 12 Mathshttps://mathsgee.com/qna/1192/evaluate-without-using-a-calculator-log-7-49-5-log-5-biggl-dfrac-1-125-biggr-13-log-9-1Fri, 24 May 2019 01:13:12 +0000Simplify $\left(\dfrac{5}{4^{-1}-9^{-1}}\right)^{\dfrac{1}{2}}+\log_3 9^{2,12}$
https://mathsgee.com/qna/1189/simplify-left-dfrac-5-4-1-9-1-right-dfrac-1-2-log3-9-2-12
Simplify $\left(\dfrac{5}{4^{-1}-9^{-1}}\right)^{\dfrac{1}{2}}+\log_3 9^{2,12}$Grade 12 Mathshttps://mathsgee.com/qna/1189/simplify-left-dfrac-5-4-1-9-1-right-dfrac-1-2-log3-9-2-12Fri, 24 May 2019 01:08:31 +0000Simplify $\log_5 125 + \dfrac{\log 32-\log 8}{\log 8}$ to a single number, without use of a calculator
https://mathsgee.com/qna/1188/simplify-log5-125-dfrac-log-32-log-8-log-8-to-a-single-number-without-use-of-a-calculator
Simplify $\log_5 125 + \dfrac{\log 32-\log 8}{\log 8}$ to a single number, without use of a calculatorGrade 12 Mathshttps://mathsgee.com/qna/1188/simplify-log5-125-dfrac-log-32-log-8-log-8-to-a-single-number-without-use-of-a-calculatorFri, 24 May 2019 01:07:37 +0000Without using a calculator, simplify $\log_3 9 - \log_5 \sqrt{5}$
https://mathsgee.com/qna/1187/without-using-a-calculator-simplify-log3-9-log5-sqrt-5
Without using a calculator, simplify $\log_3 9 - \log_5 \sqrt{5}$Grade 12 Mathshttps://mathsgee.com/qna/1187/without-using-a-calculator-simplify-log3-9-log5-sqrt-5Fri, 24 May 2019 01:06:17 +0000Given that $5^n=x$ and $n=\log_2y$ write $y$ in terms of $n$
https://mathsgee.com/qna/1185/given-that-5-n-x-and-n-log2y-write-y-in-terms-of-n
Given that $5^n=x$ and $n=\log_2y$ write $y$ in terms of $n$Grade 12 Mathshttps://mathsgee.com/qna/1185/given-that-5-n-x-and-n-log2y-write-y-in-terms-of-nFri, 24 May 2019 01:03:39 +0000Without using a calculator show that: $\log \frac{75}{16}-2\log \frac{5}{9}+\log \frac{32}{243}=\log 2$
https://mathsgee.com/qna/1184/without-using-a-calculator-show-that-log-frac-75-16-2-log-frac-5-9-log-frac-32-243-log-2
Without using a calculator show that: $\log \frac{75}{16}-2\log \frac{5}{9}+\log \frac{32}{243}=\log 2$Grade 12 Mathshttps://mathsgee.com/qna/1184/without-using-a-calculator-show-that-log-frac-75-16-2-log-frac-5-9-log-frac-32-243-log-2Fri, 24 May 2019 01:02:26 +0000Show that $\log_{a}\left(\sqrt[b]{x}\right) = \frac{\log_{a}(x)}{b}$
https://mathsgee.com/qna/1183/show-that-log-a-left-sqrt-b-x-right-frac-log-a-x-b
Show that $\log_{a}\left(\sqrt[b]{x}\right) = \frac{\log_{a}(x)}{b}$Grade 12 Mathshttps://mathsgee.com/qna/1183/show-that-log-a-left-sqrt-b-x-right-frac-log-a-x-bFri, 24 May 2019 01:01:32 +0000Show that $\log_{a}\left(\frac{x}{y}\right) = \log_{a}(x) - \log_{a}(y)$
https://mathsgee.com/qna/1182/show-that-log-a-left-frac-x-y-right-log-a-x-log-a-y
Show that<br />
$\log_{a}\left(\frac{x}{y}\right) = \log_{a}(x) - \log_{a}(y)$Grade 12 Mathshttps://mathsgee.com/qna/1182/show-that-log-a-left-frac-x-y-right-log-a-x-log-a-yFri, 24 May 2019 00:58:50 +0000Simplify the following logarithmic questions
https://mathsgee.com/qna/1170/simplify-the-following-logarithmic-questions
<p>Simplify the following logarithmic questions</p>
<ol>
<li>$\log_{2}(8^4)$</li>
<li>$\log_{8}(10^{10})$</li>
<li>$\log_{16}(x^y)$</li>
<li>$\log_{z}(y^x)$</li>
<li>$\log_{x}(y^{2x})$</li>
</ol>Grade 12 Mathshttps://mathsgee.com/qna/1170/simplify-the-following-logarithmic-questionsFri, 24 May 2019 00:46:45 +0000What does $\log_{a}(x\,.\, y) = \log_{a}(x) + \log_{a}(y)$ mean?
https://mathsgee.com/qna/1167/what-does-log-a-x-y-log-a-x-log-a-y-mean
What does $\log_{a}(x\,.\, y) = \log_{a}(x) + \log_{a}(y)$ mean?Grade 12 Mathshttps://mathsgee.com/qna/1167/what-does-log-a-x-y-log-a-x-log-a-y-meanFri, 24 May 2019 00:40:39 +0000Simplify the following using the second law of logarithms
https://mathsgee.com/qna/1166/simplify-the-following-using-the-second-law-of-logarithms
<p>Simplify the following using the second law of logarithms</p>
<ol>
<li>$\log_{2}(2)+5$</li>
<li>$\log_{10}(10)\times 100$</li>
<li>$3\times\log_{16}(16)$</li>
<li>$\log_{x}(x)+2xy$</li>
<li>$\frac{\log_{y}(y)}{x}$</li>
</ol>Grade 12 Mathshttps://mathsgee.com/qna/1166/simplify-the-following-using-the-second-law-of-logarithmsFri, 24 May 2019 00:39:38 +0000Simply the following using laws of logarithms
https://mathsgee.com/qna/1165/simply-the-following-using-laws-of-logarithms
<p>Simply the following using laws of logarithms</p>
<ol>
<li>$\log_{2}(1)+5$</li>
<li>$\log_{10}(1)\times 100$</li>
<li>$3\times\log_{16}(1)$</li>
<li>$\log_{x}(1)+2xy$</li>
<li>$\frac{\log_{y}(1)}{x}$</li>
</ol>Grade 12 Mathshttps://mathsgee.com/qna/1165/simply-the-following-using-laws-of-logarithmsFri, 24 May 2019 00:37:29 +0000Are these all the laws of logarithms?
https://mathsgee.com/qna/1164/are-these-all-the-laws-of-logarithms
<p>Are these all the laws of logarithms?</p>
<p> </p>
<ol>
<li>$\log_{a}(1)=0$</li>
<li>$\log_{a}(a)=1 $</li>
<li>$\log_{a}(x\,.\, y) = \log_{a}(x) + \log_{a}(y)$</li>
<li>$\log_{a}\left(\frac{x}{y}\right) = \log_{a}(x) - \log_{a}(y) $</li>
<li>$\log_{a}(x^b) = b \log_{a}(x)$</li>
<li>$\log_{a}\left(\sqrt[b]{x}\right) = \frac{\log_{a}(x)}{b}$</li>
</ol>
<p> </p>Grade 12 Mathshttps://mathsgee.com/qna/1164/are-these-all-the-laws-of-logarithmsFri, 24 May 2019 00:34:15 +0000Why is $\log_{2}(2)$ not the same as $\log_{10}(2)$ ?
https://mathsgee.com/qna/1161/why-is-log-2-2-not-the-same-as-log-10-2
Why is $\log_{2}(2)$ not the same as $\log_{10}(2)$ ?Grade 12 Mathshttps://mathsgee.com/qna/1161/why-is-log-2-2-not-the-same-as-log-10-2Fri, 24 May 2019 00:27:29 +0000Evaluate $\log_{7}343$
https://mathsgee.com/qna/1160/evaluate-log-7-343
Evaluate $\log_{7}343$Grade 12 Mathshttps://mathsgee.com/qna/1160/evaluate-log-7-343Fri, 24 May 2019 00:26:25 +0000Is it true that if $a^n = x$, then $\log_{a}(x) = n$ ?
https://mathsgee.com/qna/1158/is-it-true-that-if-a-n-x-then-log-a-x-n
Is it true that if $a^n = x$, then $\log_{a}(x) = n$ ?Grade 12 Mathshttps://mathsgee.com/qna/1158/is-it-true-that-if-a-n-x-then-log-a-x-nFri, 24 May 2019 00:23:29 +0000Why are logarithms commonly referred to as the inverse of exponentials?
https://mathsgee.com/qna/1157/why-are-logarithms-commonly-referred-to-as-the-inverse-of-exponentials
Why are logarithms commonly referred to as the inverse of exponentials?Grade 12 Mathshttps://mathsgee.com/qna/1157/why-are-logarithms-commonly-referred-to-as-the-inverse-of-exponentialsFri, 24 May 2019 00:22:02 +0000Evaluate the series $\sum_{n=1}^{5} 2^{-n} $
https://mathsgee.com/qna/916/evaluate-the-series-sum-n-1-5-2-n
Evaluate the series $\sum_{n=1}^{5} 2^{-n} $Grade 12 Mathshttps://mathsgee.com/qna/916/evaluate-the-series-sum-n-1-5-2-nSun, 19 May 2019 02:50:17 +0000I am 38 years old and did not pass my Matric mathematics, can I still go back to study or it is too late?
https://mathsgee.com/qna/573/i-am-38-years-old-and-did-not-pass-my-matric-mathematics-can-i-still-go-back-to-study-or-it-is-too-late
I am 38 years old and did not pass my Matric mathematics, can I still go back to study or it is too late?Generalhttps://mathsgee.com/qna/573/i-am-38-years-old-and-did-not-pass-my-matric-mathematics-can-i-still-go-back-to-study-or-it-is-too-lateTue, 12 Mar 2019 14:15:02 +0000Calculate $\sum_{k=1}^{5}4$
https://mathsgee.com/qna/120/calculate-sum-k-1-5-4
Calculate $\sum_{k=1}^{5}4$Grade 12 Mathshttps://mathsgee.com/qna/120/calculate-sum-k-1-5-4Tue, 05 Mar 2019 12:47:05 +0000The sequence $4 ; 9 ; x ; 37 ; ... $ is a quadratic sequence.
https://mathsgee.com/qna/119/the-sequence-4-9-x-37-is-a-quadratic-sequence
<p>The sequence $4 ; 9 ; x ; 37 ; ... $ is a quadratic sequence.</p>
<ol>
<li>Calculate $x$</li>
<li>Hence, or otherwise, determine the nth term of the sequence</li>
</ol>
Grade 12 Mathshttps://mathsgee.com/qna/119/the-sequence-4-9-x-37-is-a-quadratic-sequenceTue, 05 Mar 2019 12:45:34 +0000The following arithmetic sequence is given: 20 ; 23 ; 26 ; 29 ; ... ; 101
https://mathsgee.com/qna/118/the-following-arithmetic-sequence-is-given-20-23-26-29-101
<p>The following arithmetic sequence is given: $20 ; 23 ; 26 ; 29 ; ... ; 101$</p>
<ol>
<li>How many terms are there in this sequence?</li>
<li>The even numbers are removed from the sequence. Calculate the sumof terms of the remaining sequence.</li>
</ol>Grade 12 Mathshttps://mathsgee.com/qna/118/the-following-arithmetic-sequence-is-given-20-23-26-29-101Tue, 05 Mar 2019 12:43:52 +0000Evaluate $\sum_{n=1}^{20}3^{n-2}$
https://mathsgee.com/qna/116/evaluate-sum-n-1-20-3-n-2
Evaluate $\sum_{n=1}^{20}3^{n-2}$Grade 12 Mathshttps://mathsgee.com/qna/116/evaluate-sum-n-1-20-3-n-2Tue, 05 Mar 2019 12:38:19 +0000The sequence $4 ; x ; y ; 18$ is such that $ 4 ; x ; y $ form an arithmetic sequence and $x,y$ and 18 form a geometric sequence
https://mathsgee.com/qna/115/the-sequence-4-x-y-18-is-such-that-4-x-y-form-an-arithmetic-sequence-and-x-y-and-18-form-a-geometric-sequence
<p>The sequence $4 ; x ; y ; 18$ is such that $ 4 ; x ; y $ form an arithmetic sequence and $x,y$ and 18 form a geometric sequence</p>
<ol>
<li>Using the common difference of the arithmetic sequence, determine $y$ in terms of $x$</li>
<li>Using the common ratio of the geometric sequence, determine $y$ in terms of $x$</li>
<li>Hence, or otherwise, calculate the value(s) of $x$ and $y$</li>
</ol>
<p> </p>
Grade 12 Mathshttps://mathsgee.com/qna/115/the-sequence-4-x-y-18-is-such-that-4-x-y-form-an-arithmetic-sequence-and-x-y-and-18-form-a-geometric-sequenceTue, 05 Mar 2019 12:36:13 +0000The sum of the first $n$ terms of a sequence is given by $S_{n} = 2^{n = 2} - 4$
https://mathsgee.com/qna/114/the-sum-of-the-first-n-terms-of-a-sequence-is-given-by-s-n-2-n-2-4
<p>The sum of the first $n$ terms of a sequence is given by $S_{n} = 2^{n = 2} - 4$</p>
<ol>
<li>Determine the sum of the first 24 terms</li>
<li>Determine the 24th term</li>
<li>Prove that the nth term of the sequence is $2^{n + 1}$</li>
</ol>
Grade 12 Mathshttps://mathsgee.com/qna/114/the-sum-of-the-first-n-terms-of-a-sequence-is-given-by-s-n-2-n-2-4Tue, 05 Mar 2019 12:32:16 +0000Prove that $a + ar + ar^{2} + ...$(to n terms) = $\frac{a(1 - r^{n})}{1 - r}$ for $r \neq 1$
https://mathsgee.com/qna/112/prove-that-a-ar-ar-2-to-n-terms-frac-a-1-r-n-1-r-for-r-neq-1
Prove that $a + ar + ar^{2} + ...$(to n terms) = $\frac{a(1 - r^{n})}{1 - r}$ for $r \neq 1$Grade 12 Mathshttps://mathsgee.com/qna/112/prove-that-a-ar-ar-2-to-n-terms-frac-a-1-r-n-1-r-for-r-neq-1Tue, 05 Mar 2019 12:27:21 +0000Given the sequence $1 ; 2 ; 3 ; ... ; 2000$. Calculate the sum of the terms that remain when the powers of 2 are removed from the given sequence.
https://mathsgee.com/qna/108/given-the-sequence-1-2-3-2000-calculate-the-sum-of-the-terms-that-remain-when-the-powers-of-2-are-removed-from-the-given-sequence
Given the sequence $1 ; 2 ; 3 ; ... ; 2000$. Calculate the sum of the terms that remain when the powers of 2 are removed from the given sequence.Grade 12 Mathshttps://mathsgee.com/qna/108/given-the-sequence-1-2-3-2000-calculate-the-sum-of-the-terms-that-remain-when-the-powers-of-2-are-removed-from-the-given-sequenceTue, 05 Mar 2019 12:18:16 +0000$1 ; y ; b$ are the first 3 terms of an arithmetic sequence and $ 1; x ; b$ are the first 3 terms of a geometric sequence. Prove that: $$2y = x^{2} + 1$$
https://mathsgee.com/qna/107/1-y-b-are-the-first-3-terms-of-an-arithmetic-sequence-and-1-x-b-are-the-first-3-terms-of-a-geometric-sequence-prove-that-2y-x-2-1
$1 ; y ; b$ are the first 3 terms of an arithmetic sequence and $ 1; x ; b$ are the first 3 terms of a geometric sequence. Prove that: $$2y = x^{2} + 1$$Grade 12 Mathshttps://mathsgee.com/qna/107/1-y-b-are-the-first-3-terms-of-an-arithmetic-sequence-and-1-x-b-are-the-first-3-terms-of-a-geometric-sequence-prove-that-2y-x-2-1Tue, 05 Mar 2019 12:16:28 +0000$x+2$ and $x^{2} - 4$ are the first and second terms of a geometric series respectively
https://mathsgee.com/qna/106/x-2-and-x-2-4-are-the-first-and-second-terms-of-a-geometric-series-respectively
<p>$x+2$ and $x^{2} - 4$ are the first and second terms of a geometric series respectively.</p>
<p>Calculate:</p>
<ol>
<li>the value(s) of x for which the series converges</li>
<li>x if $S_{\infty} = 6$</li>
</ol>
Grade 12 Mathshttps://mathsgee.com/qna/106/x-2-and-x-2-4-are-the-first-and-second-terms-of-a-geometric-series-respectivelyTue, 05 Mar 2019 12:12:44 +0000Calculate $n$ if $\sum_{k=1}^{n} (4 - 3k) = -125$
https://mathsgee.com/qna/105/calculate-n-if-sum-k-1-n-4-3k-125
Calculate $n$ if $\sum_{k=1}^{n} (4 - 3k) = -125$Grade 12 Mathshttps://mathsgee.com/qna/105/calculate-n-if-sum-k-1-n-4-3k-125Tue, 05 Mar 2019 12:07:07 +0000A quadratic pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to -14
https://mathsgee.com/qna/104/a-quadratic-pattern-has-a-second-term-equal-to-1-a-third-term-equal-to-6-and-a-fifth-term-equal-to-14
<p>A quadratic pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to -14</p>
<ol>
<li>Calculate the second difference of this quadratic pattern</li>
<li>Hence, or otherwise, calculate the first term of the pattern.</li>
</ol>
Grade 12 Mathshttps://mathsgee.com/qna/104/a-quadratic-pattern-has-a-second-term-equal-to-1-a-third-term-equal-to-6-and-a-fifth-term-equal-to-14Tue, 05 Mar 2019 12:03:02 +0000The following sequence is a combination of an arithmetic and geometric sequence
https://mathsgee.com/qna/103/the-following-sequence-is-a-combination-of-an-arithmetic-and-geometric-sequence
<p>The following sequence is a combination of an arithmetic and geometric sequence</p>
<p>$$3 ; 3 ; 9 ; 15 ; 12 ; ...$$</p>
<ol>
<li>Write down the next TWO terms</li>
<li>Calculate $T_{52} - T_{51}$</li>
<li>Prove tha ALL the terms of this infinite sequence will be divisible by 3.</li>
</ol>
Grade 12 Mathshttps://mathsgee.com/qna/103/the-following-sequence-is-a-combination-of-an-arithmetic-and-geometric-sequenceTue, 05 Mar 2019 11:59:29 +0000Prove that for any arithmetic sequence of which the first term is $a$ and the constant difference is $d$, the sum to n terms can be expressed as
https://mathsgee.com/qna/102/prove-that-for-any-arithmetic-sequence-of-which-the-first-term-is-a-and-the-constant-difference-is-d-the-sum-to-n-terms-can-be-expressed-as
Prove that for any arithmetic sequence of which the first term is $a$ and the constant difference is $d$, the sum to n terms can be expressed as<br />
<br />
$$S_{n} =\frac{n}{2}(2a + (n-1)d)$$Grade 12 Mathshttps://mathsgee.com/qna/102/prove-that-for-any-arithmetic-sequence-of-which-the-first-term-is-a-and-the-constant-difference-is-d-the-sum-to-n-terms-can-be-expressed-asTue, 05 Mar 2019 11:56:13 +0000The first four terms of a sequence are given:
https://mathsgee.com/qna/99/the-first-four-terms-of-a-sequence-are-given
<p>The first four terms of a sequence are given
<br>
<br>
$$ \frac{2}{1 \times 2} ; \frac{2}{2 \times 3} ; \frac{2}{3 \times 4} ; \frac{2}{4 \times 5} $$</p>
<ol>
<li>Write down the next two terms of the sequence</li>
<li>Determine the nth term of the sequence.</li>
<li>Use the answer in the previous question to calculate n if the nth term is $\frac{1}{66}$</li>
</ol>
Grade 12 Mathshttps://mathsgee.com/qna/99/the-first-four-terms-of-a-sequence-are-givenTue, 05 Mar 2019 11:48:05 +0000The general term of the sequence is given by $T_{n} = an^{2} + bn + c$
https://mathsgee.com/qna/98/the-general-term-of-the-sequence-is-given-by-t-n-an-2-bn-c
<p>The general term of the sequence is given by $T_{n} = an^{2} + bn + c$</p>
<p>$$T_{2} - T_{1} = 4 $$</p>
<p>$$T_{3} - T_{2} = 6 $$</p>
<p>$$T_{4} - T_{3} = 8 $$</p>
<p> $$ T_{2} = 6$$</p>
<ul>
<li>Calculate a,b and c</li>
<li>Determine the 12th term of the sequence. </li>
</ul>
Grade 12 Mathshttps://mathsgee.com/qna/98/the-general-term-of-the-sequence-is-given-by-t-n-an-2-bn-cTue, 05 Mar 2019 11:41:17 +0000A boy arranges exercise books in piles. The first pile has 2 exercise books. The second pile has 5 exercise books.
https://mathsgee.com/qna/97/a-boy-arranges-exercise-books-in-piles-the-first-pile-has-2-exercise-books-the-second-pile-has-5-exercise-books
A boy arranges exercise books in piles. The first pile has 2 exercise books. The second pile has 5 exercise books. The third pile has 8 exercise books. The eighth pile has 22 exercise books. If the boy continues arrangig exercise books this way, calculate the total number of exercise books used if he has arranged 25 piles.Grade 12 Mathshttps://mathsgee.com/qna/97/a-boy-arranges-exercise-books-in-piles-the-first-pile-has-2-exercise-books-the-second-pile-has-5-exercise-booksTue, 05 Mar 2019 11:34:53 +0000