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The next term of the G.P. x ,x^2+2,a n d...

The next term of the G.P. `x ,x^2+2,a n dx^3+10` is `(729)/(16)` b. `6` c. `0` d. `54`

A

`729/16`

B

6

C

0

D

54

Text Solution

Verified by Experts

The correct Answer is:
A, D
`x,x^(2)+2,x^(3)+10` are in G.P. Hence,
`x(x^(3)+10)=(x^(2)+2)^(2)=x^(4)+4x^(2)+4`
`rArr4x^(2)-10x+4=0`
or `2x^(2)-5x+2=0`
or `x=2,1/2`
The 4th term of G.P. is
`(x^(3)+10)r=(x^(3)+10)((x^(2)+2)/x)`
`={{:(54 " when " x=2),(729/16" when "x=1/2):}`
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