The sums of `n` terms of three arithmetical progressions are `S_1, S_2` and `S_3dot` The first term of each unityand the common differences are `1,2` and `3` respectively. Prove that `S_1+S_3=2S_2dot`

Explanation

To solve the problem, we need to find the sums of the first \( n \) terms of three arithmetic progressions (APs) and then prove that \( S_1 + S_3 = 2S_2 \).

### Step 1: Define the parameters of the APs
- For the first AP:
- First term \( a_1 = 1 \)
- Common difference \( d_1 = 1 \)

- For the second AP:
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