Question

For what value of k will the consecutive terms 2k + 1, 3k + 3 and 5k − 1 form an A.P.?

Answer 1

The given terms are 2k + 1, 3k + 3 and 5k − 1.
The differences between the consecutive terms are
3k + 3 − (2k + 1) = k + 2 = d₁
and
5k − 1 − (3k + 3) = 2k − 4 = d₂
If the given terms are in an AP, then
d₁ = d₂
⇒ k + 2 = 2k − 4
⇒ k = 6
Hence, the value of k for which the given terms are in an AP is 6.