Question

FOR WHAT VALE 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+b=2b

k+9+2k+7−2(2k−1)

⇒ 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 A.P