Question

if the sum of n terms of an A.P is 5n²+2n, find the series?

Answer 1

Dear Student!

Here is the answer to your question.

S_n = 5n² + 2n

S₁ = a₁

a₁ = 5(1)² + 2(1) = 5 × 1 + 2 × 1 = 5 + 2 = 7

S₂ = 5(2)² + 2(2) = 5 × 4 + 4 = 20 + 4 = 24

a₂ = S₂ – a₁ = 24 – 7 = 17

S₃ = 5(3)² + 2(3) = 5 × 9 + 6 = 45 + 6 = 51

a₃ = S₃ – S₂ = 51 – 24 = 27

∴T₁ or a₁ = 7, a₂ = 17, a₃ = 27

d = a₃ – a₂ = 27 – 17 = 10

We know that

a_n = a + (n – 1)d

a_n = 7 + (n – 1).10 = 7 + 10n – 10 = 10n – 3

Thus, the series will be as follows,

7 + 17 + 27 + 37 + 47 + … + (10n – 3)+ …

Cheers!