Find the sum of the series : `3+5+7+6+9+12+9+13+17+.... +3n` terms.

Explanation

To find the sum of the series \(3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + \ldots + 3n\), we first need to identify the pattern in the series.

### Step 1: Identify the Pattern
The series can be divided into three distinct arithmetic progressions (APs):
1. **First AP**: \(3, 6, 9, \ldots\)
2. **Second AP**: \(5, 9, 13, \ldots\)
3. **Third AP**: \(7, 12, 17, \ldots\)

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