JEE Mains · Maths · STD 11 - 8. sequence and series
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-
- A \(980\)
- B \(960\)
- C \(960\)
- D \(970\)
Answer & Solution
Correct Answer
(D) \(970\)
Step-by-step Solution
Detailed explanation
\(1+d, \quad 1+7 d, 1+43 d \text { are in GP } \) \( (1+7 d)^2=(1+d)(1+43 d) \) \( 1+49 d^2+14 d=1+44 d+43 d^2 \) \( 6 d^2-30 d=0 \) \( d=5 \) \( S_{20}=\frac{20}{2}[2 \times 1+(20-1) \times 5] \) \(=10[2+95] \) \(=970\)
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