The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.

Explanation

To solve the problem step by step, we will use the properties of arithmetic progressions (AP).

### Step 1: Define the terms of the AP
Let the first term of the AP be \( a \) and the common difference be \( d \).

### Step 2: Write the expressions for the third and seventh terms
The \( n \)-th term of an AP is given by:
\[
...