Find the sum to n terms of the series :`3xx1^2+5xx2^2+7xx3^2+dotdotdot`

Explanation

To find the sum to n terms of the series \(3 \times 1^2 + 5 \times 2^2 + 7 \times 3^2 + \ldots\), we can follow these steps:

### Step 1: Identify the nth term of the series
The series can be expressed in terms of its nth term. Observing the pattern:
- The first term is \(3 \times 1^2\) which can be rewritten as \( (2 \times 1 + 1) \times 1^2\)
- The second term is \(5 \times 2^2\) which can be rewritten as \( (2 \times 2 + 1) \times 2^2\)
- The third term is \(7 \times 3^2\) which can be rewritten as \( (2 \times 3 + 1) \times 3^2\)

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