Question

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

Answer 1

This is required that

k+9 , 2k-1 , 2k+7 are three consecutive terms of an ap

Let common difference of that AP is d.

So ,,,,

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

⇒ k-10=8

⇒k=18

Answer 2

This is required that  

k+9 , 2k-1 , 2k+7 are three consecutive terms of an ap

Let common difference of that AP is d.

 So ,,,,

 (2k-1) -(k+9) = d= (2k+7)-(2k-1)

⇒ k-10=8

⇒k=18