If `a_(m)` be the mth term of an AP, show 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 statement \( a_1^2 - a_2^2 + a_3^2 - a_4^2 + \ldots + a_{2n-1}^2 - a_{2n}^2 = \frac{n}{2n-1}(a_1^2 - a_{2n}^2) \), we will start by analyzing the left-hand side (LHS) and simplifying it step by step.

### Step 1: Write down the LHS
The left-hand side of the equation is given by:
\[ LHS = a_1^2 - a_2^2 + a_3^2 - a_4^2 + \ldots + a_{2n-1}^2 - a_{2n}^2 \]

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