Question

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 : (1) `8/5` (2) `4/3` (3) 1 (4) `7/4`
A. `4/3`
B. 1
C. `7/4`
D. `8/5`

Answer 1

Correct Answer - A
Given a+d,a+4d,a+8d are in G.P.
`therefore (a+4d)^(2)=(a+d)(a+8d)=a^(2)+9ad+8d^(2)`
`rArr8d^(2)=adrArra=8d`
`therefore9d,12d,16d` are G.P.
Common ratio `r=12/9=4/3`