Question

Find the value of n if 2n + 1 , (n)square + n + 1 , (3n)square - 3n + 3 are consecutive terms of AP.

Answer 1

n = 2 or n = 1.

Step-by-step explanation:

There are three terms of n:

(2n + 1), (n² + n + 1) and (3n² - 3n + 3)

Now, it is given that the three terms are in A.P.

So, they will have an equal common difference.

Hence, we can write,

(3n² - 3n + 3) - (n² + n + 1) = (n² + n + 1) - (2n + 1)

⇒ 2n² - 4n + 2 = n² - n

⇒ n² - 3n + 2 = 0

⇒ n² - 2n - n + 2 = 0

⇒ (n - 2)(n - 1) = 0

Therefore, n = 2 or n = 1. (Answer)