Question

If the sum of first n terms of an AP is n², then find its 10th term.

Answer 1

We know sum of n terms of an AP is 

S_n = n² 

For n = 1, S₁ = (1)² = 1

So, a₁ = 1

For n = 2, S₂ = (2)² = 4

For n = 3, S₃ = (3)² = 9

S₂ - S₁ = a₂ 

⇒ a₂ = 4 - 1 = 3

So, d = a₂ - a₁ = 3 - 1 = 2

We knopw nth term of an AP is

a_n = a + (n - 1)d

For n = 10

a₁₀ = 1 + (10 - 1)2

⇒ a₁₀ = 1 + 9 × 2

⇒ a₁₀ = 19

Thus, the 10th term of the AP is 19.