If S(n) denotes the sum of n terms of an...

If `S_(n)` denotes the sum of `n` terms of an A.P., `S_(n +3) - 3S_(n + 2) + 3S_(n + 1) - S_(n) =`

A

`2s_n`

B

`S_(n+1)`

C

`3S_n`

D

0

Text Solution

Verified by Experts

The correct Answer is:

D

`S_(n+3)-3S_(n+2)+3S_(n+1)-S_(n)`
`=(S_(n+3)-S_(n+2))-2(S_(n+2)-S_(n-1))+(S_(n+1)-S_(n))`
=`T_(n+3)-2T_(n+2)+T_(n+1)`
`=(T_(n+3)-T_(n+2))-(T_(n+2)-T_(n+1))`
=d-d=0

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