Say whether the expression is equal or not — task. Maths CBSE Live product, Class 10 (2026-27).

If the sum of first \(n\), \(2n\) and \(3n\) terms of an \(A.P.\) are \(S_1\), \(S_2\) and \(S_3\) respectively, then show that \(S_3 = 3 (S_2 - S_1)\).

Explanation:

The general term for the sum of \(n\) terms of the series is

S_{n} = \frac{i}{i} [i i + (i - i) i]

This implies,

S_{1} = \frac{i}{i} [i i + (i - i) i]

S_{2} = \frac{i i}{i} [i i + (i i - i) i]

S_{3} = \frac{i i}{i} [i i + (i i - i) i]

Thus, we have:

S_{2} - S_{1} = \frac{i}{i} [i i + (i i - i) i]

3 (S_{2} - S_{1}) = \frac{i i}{i} [i i + (i i - i) i]

Therefore,

3 (S_{i} - S_{i}) = S_{i}

Hence, proved.

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