Determine `k`, so that `k^(2)+4k+8, 2k^(2)+3k+6` and `3k^(2)+4k+4` are three consecutive terms of an AP.

Explanation

To determine the value of \( k \) such that the expressions \( k^2 + 4k + 8 \), \( 2k^2 + 3k + 6 \), and \( 3k^2 + 4k + 4 \) are three consecutive terms of an Arithmetic Progression (AP), we can follow these steps:

### Step 1: Define the terms
Let:
- \( A_1 = k^2 + 4k + 8 \)
- \( A_2 = 2k^2 + 3k + 6 \)
- \( A_3 = 3k^2 + 4k + 4 \)

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