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For sequence (t(n)), if S(n)=5(2^(n)-1) ...

For sequence `(t_(n)),` if `S_(n)=5(2^(n)-1)` then `t_(n)=` . . .

A

`5(2^(n+1))`

B

`(5xx2^(n))/(4)`

C

`5(2^(n-1))`

D

`(2(2^(n-1)))/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `S_(n)=5(2^(n)-1)`
We know that, `a_(n)=S_(n)-S_(n-1)`
`=5(2^(n)-1)-5(2^(n-1)-1)`
`=5(2^(n)-2^(n-1))`
`=5(2^(n-1))`
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