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

k = 18

the common difference d of an arithmetic sequence is

d = a₂ - a₁ = a₃ - a₂ = ...

a₂ - a₁ = 2k - 1 - k - 9 = k - 10 and

a₃ - a₂ = 2k + 7 - (2k - 1) = 2k + 7 - 2k + 1 = 8, hence

k - 10 = 8 ⇒ k = 8 + 10 = 18

the 3 consecutive terms are

27, 35, 43