If the sequence `a_(1),a_(2),a_(3),…,a_(n)` is an A.P., then prove that `a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))`

Explanation

To prove the equation

\[ a_1^2 - a_2^2 + a_3^2 - a_4^2 + \ldots + a_{2n-1}^2 - a_{2n}^2 = \frac{n}{2n-1}(a_1^2 - a_{2n}^2) \]

given that the sequence \(a_1, a_2, a_3, \ldots, a_n\) is an arithmetic progression (A.P.), we can follow these steps:

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