Question

If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is

(a) −2
(b) 3
(c) −3
(d) 6

Answer 1

Since, k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P.

Then, Second term − First term = Third term − Second term = d (common difference)
⇒ 2k − 1 − k = 2k + 1 − (2k − 1)
⇒ k − 1 = 2k + 1 − 2k + 1
⇒ k − 1 = 2
⇒ k = 2 + 1
⇒ k = 3

Hence, the correct option is (b).