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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)/((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))`

Text Solution

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VIKAS GUPTA (BLACK BOOK) ENGLISH-SEQUENCE AND SERIES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
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