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.