Question

If n – 2, 4n – 1 and 5n + 2 are in A.P., then n = ______.

Answer 1

If n – 2, 4n – 1 and 5n + 2 are in A.P., then n = 1.

Explanation:

Property: for three numbers in A.P. the middle term equals the average of the other two.

So 2(4n – 1) = (n – 2) + (5n + 2)

⇒ 8n − 2 = 6n

⇒ 2n = 2 

⇒ n = 1

Check: n = 1 gives –1, 3, 7, which have common difference 4, so they are in A.P.