If `S_(n)` denotes sum of first `n` tem of a series and if `S_(n+2)-S_(n)=n^(2)` then `S_(20)` is `("given that" T_(1)+T_(2)=0)`

Options

A. `1540`
B. `1140`
C. `770`
D. `1120`

Answer

B

Explanation

If `S_(n)` denotes …………
`S_(n+2)-S_(n)=n^(2)`
`T_(n+2)+T_(n+1)=n^(2)`
`T_(1)+T_(2)=0`
`T_(3)+T_(2)=1`
`T_(4)+T_(3)=4`
`T_(5)+T_(4)=9`
and so on
Now sequence is
`T_(1), -T_(1), 1+T_(1),3-T_(1),6+T_(1),10-T_(1)`.............
`i.e. S_(20) = T_(1)-T_(2)+1+3+6+10+` ....... up to 20 terms
`S_(20 = 1+3+6+10+` ......... up 18 terms
`S_(20) = sum_(r=1)^(18)(r^(2))/(2)+(r )/(2)`
`S_(20) = 1140`.