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If t2 and t3 of a GP are p and q, respec...

If `t_2 and t_3` of a GP are `p and q`, respectively, then `t_5= `__________.

A

`p((q)/(p))^(3)`

B

`p((q)/(p))^(2)`

C

`(p^(2))/(q^(3))`

D

`p^(2)q^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`t_2 = ar =p`
`t_3 = ar^(2) = q`
`rArr (t_3)/(t_2) = (q)/(p) = (ar^(2))/(ar) rArr r= (q)/(p)`
`ar =p`
`rArr a *(q)/(p) = p rArr a = (p^(2))/(q)`
`t_5 =a*r^(4)`
`= (p^(2))/(q) ((q)/(p))^(4)`
` = (p^(2))/(q) xx (q^(4))/(p^(4)) = (q^(3))/(p^(2)) = p ((q)/(p))^(3)`
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