Question

for what value of k will k+9 , 2k -1 and 2k +7 are the consecutive terms of an AP ????

Answer 1

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

For k = 18, the terms k+9 , 2k - 1 , 2k + 7 are in AP

Hope This helps you!

Answer 2

common difference : d = 2k -1 - (k+9)  =  2k+7 - (2k-1)
                                        k - 10 = 8
                                        k = 18