Question

find the value of k if 2 k, k + 10 and 3 k + 2 are in AP

Answer 1

Difference of consecutive terms in an AP is constant.

so,
(3k+2)-(k+10)=(k+10)-2k

2k-8=-k+10
3k=18
k=6.
done.
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Answer 2

k+10-2k = 3k+2- k-10
-k+10= 4k-8
5k=18
k = 18/5= 3.6