If Sn, denotes the sum of n terms of an ...

If `S_n,` denotes the sum of `n` terms of an `A.P.`, then `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

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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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