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Lets take each term as a, a2 and a3.
if they are terms of an AP then a2- a = a3 - a2
2k^ + 3k + 6 - (k^ + 4k + 8)= 3k^ + 4k + 4 - (2k^ + 3k + 6)
2k^ - k^ + 3k - 4k + 6 - 8 = 3k^ - 2k^ + 4k - 3k + 4 - 6
k^ - k - 2 = k^ + k - 2
2k = 0
k = 0
if they are terms of an AP then a2- a = a3 - a2
2k^ + 3k + 6 - (k^ + 4k + 8)= 3k^ + 4k + 4 - (2k^ + 3k + 6)
2k^ - k^ + 3k - 4k + 6 - 8 = 3k^ - 2k^ + 4k - 3k + 4 - 6
k^ - k - 2 = k^ + k - 2
2k = 0
k = 0
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