The given three consecutive terms of AP are k, 2k – 1 and 2k + 1.
We know that if a, b and c are in AP, then 2b = a + c.
⇒ 2 (2k – 1) = k + 2k + 1
⇒ 4k – 2 = 3k + 1
⇒ 4k – 3k = 1 + 2
⇒ k = 3
∴ The value of k is 3.
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