JEE Mains · Maths · STD 11 - 8. sequence and series
Let the first three terms \(2, p\) and \(q\), with \(q \neq 2\), of a \(G.P.\) be respectively the \(7^{\text {th }}, 8^{\text {th }}\) and \(13^{\text {th }}\) terms of an \(A.P.\) If the \(5^{\text {th }}\) term of the \(G.P.\) is the \(\mathrm{n}^{\text {th }}\) term of the \(A.P.\), then \(\mathrm{n}\) is equal to
- A \(151\)
- B \(169\)
- C \(177\)
- D \(163\)
Answer & Solution
Correct Answer
(D) \(163\)
Step-by-step Solution
Detailed explanation
\( 2=a+6 d \quad \ldots(\text { i) } \) \( p=a+7 d \quad \ldots \text { (ii) } \) \( q=a+12 d \quad \ldots \text { (iii) } \) \( p-2=d \) \(((ii)-(i))\) \( q-p=5 d \) \(((iii)-(ii))\) \( q-p=5(p-2) \) \( q=6 p-10 \) \( p^2=2(6 p-10) \) \( p^2-12 p+20=0 \) \( p=10,2 \)…
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