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Let b(1),b(2),....... be a gemoertic seq...

Let `b_(1),b_(2),.......` be a gemoertic sequence such that `b_(1)+b_(2)=1and sum_(k=1)^(oo)b_(k)=2`. Given that `b_(2)lt0` then the value of `b_(1)` is :

A

`2-sqrt2`

B

`1+sqrt2`

C

`2+sqrt2`

D

`4-sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
C
`b_(1),b_(2),b_(3)`
`a,ar,ar^(2)...........`
`a+ar=1impliesa=(1)/((1+r))`
`sum_(k=1)^(oo)b_(k)=2implies(a)/(1-r)=2`
`(1)/(1-r^(2))=2`
`r^(2)=(1)/(2)impliesr=pm(1)/(sqrt2)`
`b_(2)lt0impliesr=-(1)/(sqrt2)impliesa=b_(1)=2+sqrt2`
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