Question

If the nth term of an AP is (2n + 1) then find the sum of its first three terms

If the n^th term of an A.P. is (2n + 1), then the sum of its first three terms is

Options

• A. 6n + 3

• B. 15

• C. 12

• D. 21

Answer 1

∵ a_n = 2n + 1

a₁ = 2(1) + 1 = 3

a₂ = 2(2) + 1 = 5

a₃ = 2(3) + 1 = 7

∴ a₁ + a₂ + a₃ = 3 + 5 + 7 = 15

Answer 2

Given: The n^th term of A.P. i.e., a_n = 2n + 1

To find: Sum of first three terms

On putting n = 1, 2 and 3, we obtain:

a₁ = 2 × 1 + 1 = 2 + 1 = 3

a₂ = 2 × 2 + 1 = 4 + 1 = 5

a₃ = 2 × 3 + 1 = 6 + 1 = 7

∴ Sum of first three terms a₁ + a₂ + a₃ = 3 + 5 + 7 = 15

Hence, the correct answer is B.