If x1, x2, x3,...... x (2n) are in A.P...

If `x_1, x_2, x_3,...... x _(2n)` are in `A.P`, then `sum _(r=1)^(2n) (-1)^(r+1) x_r^2` is equal to (a) `(n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2))` (b) `(2n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2))` (c) `(n)/((n-1))(x _(1)^(2) -x _(2n) ^(2))` (d) `(n)/((2n+1))(x _(1)^(2) -x _(2n) ^(2))`

A

`n/(n-1)(x_1^2 -x_(2n)^2)`

B

`(2n)/(2n-1)(x_1^2-x_(2n)^2)`

C

`n/((2n-1))(x_1^2 -x_(2n)^2)`

D

`n/(n+1)(x_1^2 -x_(2n)^2)`

Text Solution

Verified by Experts

The correct Answer is:

C

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