JEE MAIN - Mathematics (2024 - 31st January Evening Shift - No. 14)
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 a G. P. If the first term of the A. P. is 1, then the sum of its first 20 terms is equal to -
990
980
960
970
Explanation
$$\begin{aligned}
& 1+d, \quad 1+7 d, 1+43 d \text { are in GP } \\
& (1+7 d)^2=(1+d)(1+43 d) \\
& 1+49 d^2+14 d=1+44 d+43 d^2 \\
& 6 d^2-30 d=0 \\
& d=5 \\
& S_{20}=\frac{20}{2}[2 \times 1+(20-1) \times 5] \\
& \quad=10[2+95] \\
& \quad=970
\end{aligned}$$
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