Permutations And Combinations

Question
CBSEENMA11015448

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

  • 8/5

  • 4/3

  • 1

  • 7/4

Solution

B.

4/3

Let a be the first term and d be a common difference. Then, we have a+d, a+4d, a+8d in GP,
ie. (a +4d)2 = (a+d)(a+8d)
⇒ a2 +16d2 +8ad = a2 +8ad +ad +8d2
⇒ 8d2 = ad
8d =a  [∴ d≠0]
Now, common ratio,
fraction numerator straight a plus 4 straight d over denominator straight a plus straight d end fraction space equals space fraction numerator 8 straight d space plus 4 straight d over denominator 8 straight d space plus straight d end fraction space equals space fraction numerator 12 straight d over denominator 9 straight d end fraction space equals space 4 over 3

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Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.