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JEE Mains · Maths · STD 11 - 8. sequence and series
If the \(2^{nd}\,, \,5^{th}\,\, and \,\,9^{th}\) terms of a non-constant \(A.P.\) are in \(G.P.\), then the common ratio of this \(G.P.\) is :
- A \(1\)
- B \(\frac{7}{4}\)
- C \(\frac{8}{5}\)
- D \(\frac{4}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{4}{3}\)
Step-by-step Solution
Detailed explanation
Let the terms of \(AP\) be \(A + d, A + 4d, A + 8d\) Let the \(GP\) be \(a, ar, ar^2\) \(a = A + d\) \(ar = A + 4d\) \(ar^2= A + 8d\) \(\frac{{a{r^2} - ar}}{{ar - a}} = \frac{{(A + 8d) - (A + 4d)}}{{(A + 4d) - (A + d)}} \)\(= \frac{4}{3}\) \(r= \frac{4}{3}\)
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