The $$\(n\)$$th term of an arithmetic progression is $$\(\frac{1}{2}(3 n-15)\)$$. Find the value of $$\(n\)$$ for which the sum of the first $$\(n\)$$ terms is 84 . ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s20_qp_12 Year：2020 Question No：4
Answer:
1 st term is \(-6,2\) nd term is \(-4.5\)
(M1 for using \(k\) th terms to find both \(a\) and \(d\) )
\[
\begin{array}{l}
\rightarrow a=-6, d=1.5
S_{n}=84 \rightarrow 3 n^{2}-27 n-336=0
\end{array}
\]
Solution \(n=16\)
(M1 for using \(k\) th terms to find both \(a\) and \(d\) )
\[
\begin{array}{l}
\rightarrow a=-6, d=1.5
S_{n}=84 \rightarrow 3 n^{2}-27 n-336=0
\end{array}
\]
Solution \(n=16\)
Knowledge points:
1.1.3 solve quadratic equations, and quadratic inequalities, in one unknown (By factorising, completing the square and using the formula.)
1.6.3 use the formulae for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions (Including knowledge that numbers a,b,c are 'in arithmetic progression' if 2 b=a+c (or equivalent) and are 'in geometric progression' if (or equivalent) (Questions may involve more than one progression.)
Solution:
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