If the sum of n terms of an arithmetic progression S_n = n² - n, then the third term of the series is :

1. 2

2. 4

3. 6

4. 9

Given,

Sum of n terms of an arithmetic progression S_n = n² - n.

S₁ = 1² - 1 = 0,

S₂ = 2² - 2 = 4 - 2 = 2,

S₃ = 3² - 3 = 9 - 3 = 6.

Sum upto first term = First term = 0.

Given, sum upto 2 terms = 2 and first term = 0, second term = 2.

Sum upto third term = 6

∴ First term + Second term + Third term = 6

⇒ 0 + 2 + Third term = 6

⇒ Third term = 6 - 2 = 4.

Hence, Option 2 is the correct option.