Sequences and Series 3 Question 7

7. If the 2nd,5 th and 9 th terms of a non-constant AP are in GP, then the common ratio of this GP is (2016 Main)

(a) 85

(b) 43

(c) 1

(d) 74

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Answer:

Correct Answer: 7. (d)

Solution:

  1. Let a be the first term and d be the common difference.

Then, we have a+d,a+4d,a+8d in GP,

i.e. (a+4d)2=(a+d)(a+8d)

a2+16d2+8ad=a2+8ad+ad+8d2

8d2=ad

8d=a

[d0]

Now, common ratio,

r=a+4da+d=8d+4d8d+d=12d9d=43



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