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If 2nd, 3rd and 6th terms of an AP are t...

If 2nd, 3rd and 6th terms of an AP are the three consecutive terms of a GP then find the common ratio of the GP.

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The correct Answer is:
3
`(a+d), (a+2d), (a+5d)` are in GP.
`:. (a+2d)/(a+d)=(a+5d)/(a+2d) rArr (a+2d)^(2)=(a+d)(a+5d)`
`rArr d^(2)+2ad=0 rArr d(d+2a)=0rArr d=-2a" "[ :' d ne 0]`
So, these terms are `=a, -3a, -9a`. Its common ratio `=(-3a)/(-a)=3`.
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