Question

For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P?

Answer 1

Answer:

• k = 18.

Step-by-step explanation:

We have,

=> a = k + 9

=> b = 2k - 1

=> c = 2k + 7

We know,

For a progression to be in A.P, we have 2b = a + c

Hence,

⇒ 2(2k - 1) = (k + 9) + (2k + 7)

⇒ 4k - 2 = k + 9 + 2k + 7

⇒ 4k - k - 2k = 7 + 9 + 2

⇒ k = 18

∴ The value of k is 18.

We know,

a_2 - a_1 = a_3  - a_2

Hence,

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

⇒ 2k - 1 - k - 9 = 2k + 7 - 2k + 1

⇒ 3k - 2k = 1 + 7 + 9 + 1

⇒ k = 18

∴ The value of k is 18.