Question

If the sum of ‘n’ terms of a series is (5n² + 3n), then find its first five terms.

Answer 1

The first term of a series is always equal to the sum of the first term (S₁).

1. a₁ = S₁ = 5(1)² + 3(1)

a₁ = 5(1) + 3

a₁ = 8

2. S₂ = 5(2)² + 3(2)

= 5(4) + 6

= 20 + 6

= 26

a₂ = S₂ − S₁

= 26 − 8

a₂ = 18

3. S₃ = 5(3)² + 3(3)

= 5(9) + 9

= 45 + 9

= 54

a₃ = S₃ − S₂

= 54 − 26

a₃ = 28

4. S₄ = 5(4)² + 3(4)

= 5(16) + 12

= 80 + 12

= 92

a₄ = S₄ − S₃

= 92 − 54

a₄ = 38

5. S₅ = 5(5)² + 3(5)

= 5(25) + 15

= 125 + 15

= 140

a₅ = S₅ − S₄

= 140 − 92

a₄ = 48

The first five terms of the series are 8, 18, 28, 38, 48.