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: Set up the condition for an AP
For three terms \( a \), \( b \), and \( c \) to be in AP, the condition is:
\[ b - a = c - b \]
In our case, we have:
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