If (p + 1)th term of an A.P. is twice the (q + 1)th term, then prove that (3p + 1) th term will be twice the (p + q + 1)th term.

Explanation

To prove that the \((3p + 1)\)th term of an A.P. is twice the \((p + q + 1)\)th term, given that the \((p + 1)\)th term is twice the \((q + 1)\)th term, we can follow these steps:

### Step 1: Express the terms of the A.P.
The \(n\)th term of an A.P. can be expressed as:
\[ T_n = a + (n - 1)d \]
where \(a\) is the first term and \(d\) is the common difference.
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