If nth term of an A.P. is (2n + 1), what is the sum of its first three terms? (CBSE 2012)

Given: nth term of an A.P. is (2n + 1),

To find: the sum of its first three terms

Explanation: given nth term of an A.P. is (2n + 1),

∴ a_n = 2n + 1……….(i)

Now the first term of the AP can be found by substituting n = 1, so we get

a₁ = 2 × 1 + 1

= 2 + 1

a₁ = 3………(ii)

Now the second term of the AP can be found by substituting n = 2, so we get

a₂ = 2 × 2 + 1

= 4 + 1

a₂ = 5………(iii)

Now the third term of the AP can be found by substituting n = 3, so we get

a₃ = 2 × 3 + 1

= 6 + 1

a₃ = 7………(iv)

So, the sum of the first three terms of the AP is

a₁ + a₂ + a₃

Now substituting values from equation (ii), (iii) and (iv) we get

a₁ + a₂ + a₃ = 3 + 5 + 7

= 15

Hence the sum of its first three terms is 15.