Answer :

Let a1 = k2 + 4k + 8


a2 = 2k2 + 3k + 6


a3 = 3k2 + 4k + 4


Three terms will be in an AP if


a2 - a1 = a3 - a2


2k2 + 3k + 6 - (k2 + 4k + 8) = 3k2 + 4k + 4 - (2k2 + 3k + 6)


k2 - k - 2 = k2 + k - 2


2k = 0


k = 0


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