Find the 6^th term of an AP, if the sum of first n terms is n2 + n

Question

Question

Answer 1

Concept:

The formula for the nth term of an AP is given by: T_n = S_n - S_{n - 1}

Where S_n is the sum of first n terms of AP and S_{n - 1} is the sum of first (n - 1) terms of AP

Calculation:

Given: the sum of first n terms of AP is n2 + n

To Find: T6 =?

S_n = n2 + n

S₆ = 6² + 6 = 42

Similarly

S₅ = 5² + 5 = 30

Now,

Tn = Sn - Sn - 1

∴ T₆ = S₆ - S₅

= 42 - 30

= 12

Hence, option (3) is correct.