Question

If the sum of n terms of an arithmetic progression S_n = n² – n, then the third term of the series is ______.

Options

• 2

• 4

• 6

• 9

Answer 1

If the sum of n terms of an arithmetic progression S_n = n² – n, then the third term of the series is 4.

Explanation:

For any series the nth term a_n = S_n – S_{n – 1}. 

Here, S_n = n² – n.

So, S_{n – 1} = (n – 1)² – (n – 1)

And a_n = (n² – n) – [(n – 1)² – (n – 1)]

= 2n – 2

Thus, a₃ = 2 × 3 – 2 = 4.