Let `a_1,a_2,a_3…… ,a_n ` be in G.P such that `3a_1+7a_2 +3a_3-4a_5=0` Then common ratio of G.P can be

Options

A. 2
B. `3/2`
C. `5/2`
D. `-1/2`

Answer

B, D

Explanation

Given
`3a_(1)+7a_(2)+3a_(3)-4a_(5)=0`
`rArr7(a_(1)+a_(2)+a_(3))=4(a_(1)+a_(3)+a_(5))`
`rArr7(1+r+r^(2))=4(1+r^(2)+r^(4))`
`rArr7=4(r^(2)-r+1)`
`rArr4r^(2)-4r+1=4`
`rArr(2r-1)^(2)=4`
`rArr2r-1=pm2`
`rArrr=3//2,-1//2`