Question

let the sequence a1,a2.... .an.......form an A.P. . Then a1^2 -a2^2 + a3^2 - a4^2 + .......- a2n^2 is equal to ???

Answer 1

Since the terms form an ap, the difference of two consecutive terms will always be equal to the common difference.
${a1}^{2} - {a2}^{2} \\ = (a1 + a2)(a1 - a2) \\ = (a1 + a2)( - d)$
Now we see that (-d) is common in all these terms as we group them together, and the number of terms won't be a problem since 2n is an even number. So we can simplify it to
$= - d(a1 + a2 + ......a2n) \\ = -dn(2a + (2n - 1)d)$
Hope this helps, if it does, mark it as the brainliest answer.

Answer 2

Answer:

hope it will help.if help make it brainlist answer.