If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Explanation

To solve the problem, we will use the formula for the sum of the first n terms of an arithmetic progression (AP):

\[ S_n = \frac{n}{2} \left(2a + (n - 1)d\right) \]

where:
- \( S_n \) = sum of the first n terms
- \( a \) = first term
- \( d \) = common difference
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