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The first three terms of a sequence are ...

The first three terms of a sequence are `3,-1,-1`. The next terms are

A

`2`

B

`-3`

C

`-(5)/(27)`

D

`-(5)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
B
The given sequence is not an AP or GP or HP. It is an AGP,`3,(3+d)r,(3+2d)r^(2),"…."`
`implies (3+d)r=-1,(3+2d)r^(2)=-1`
Eliminating r, we get `(3+d)^(2)=-(3+2d)`
`implies d^(2)+8d+12=0 implies d=-2,-6`
then `r=-1,(1)/(3)`
`:.` next term is `(3+3d)r^(3)=3,-(5)/(9)`
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