Question

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

Answer 1

For an AP , common difference must be same .

we know that ,

• b - a = c - b

=> 2b = a + c

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

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

=> 4k -2 = 3k + 16

=> 4k - 3k = 16 +2

=> k = 18

Answer 2

Answer:

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