Question

For what value of k will k+9,2k-1&2k+7 are the consecutive term of an ap

Answer 1

If k+9, 2k-1 and 2k+7 are in AP then their common difference will be the same.
So,
2k-1-k-9=2k+7-2k+1
k-10=8
k=18

Answer 2

Since they are in AP,

The common difference is constant

T3 - T2 = T2 - T1

=> 2k+7 - (2k-1) = 2k-1 - (k+9)

=> 2k +7 - 2k +1 = 2k - 1 - k - 9

=> 8 = k - 10

=> k = 18