Question

For what value of K will K+9,2k-1and 2k+7 are consecutive terms of an ap??

Answer 1

2k-1-(k+9)=2k+7-(2k-1)
2k-1-k-9=2k+7-2k+1
k-10=8
k=18

Answer 2

Let,
k + 9 = a
2k - 1 = b
2k + 7 = c

To be in AP,

a + c = 2b
(k + 9) + (2k + 7) = 2(2k - 1)
k + 9 + 2k + 7 = 4k - 2
3k + 16 = 4k - 2
3k - 4k = - 2 - 16
- k = - 18
k = 18