Sequences And Series Question 17
Question 17 - 2024 (31 Jan Shift 2)
Let $2^{\text {nd }}, 8^{\text {th }}$ and $44^{\text {th }}$, terms of a non-constant A.P. be respectively the $1^{\text {st }}, 2^{\text {nd }}$ and $3^{\text {rd }}$ terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to-
(1) 980
(2) 960
(3) 990
(4) 970
Show Answer
Answer (4)
Solution
$$ \begin{aligned} & 1+d, 1+7 d, 1+43 d \text { are in GP } \\ & (1+7 d)^{2}=(1+d)(1+43 d) \\ & 1+49 d^{2}+14 d=1+44 d+43 d^{2} \\ & 6 d^{2}-30 d=0 \\ & d=5 \\ & S _{20}=\frac{20}{2}[2 \times 1+(20-1) \times 5] \\ & \quad=10[2+95] \\ & \quad=970 \end{aligned} $$
