The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum first ten terms of this AP is 235, find the sum of its first twenty terms.

Explanation

To solve the problem step by step, we will use the formulas for the sum of the first n terms of an arithmetic progression (AP).

### Step 1: Write the formulas for the sums of the first n terms of an AP
The sum of the first n terms of an AP can be calculated using the formula:
\[ S_n = \frac{n}{2} \times (2a + (n-1)d) \]
where \( S_n \) is the sum of the first n terms, \( a \) is the first term, \( d \) is the common difference, and \( n \) is the number of terms.
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