Question

The second term of an arithmetic series is 12 and the third term 17.find the sum of the first 30 terms

Answer 1

S₃₀ = 2385

Explanation:

the sum to n terms of an arithmetic series is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

a₁ is the first term, d is the common difference , n the term number

To calculate S₃₀ , we require a₁ and d

given a₂ = 12 and a₃ = 17 , then

d = a₃ - a₂ = 17 - 12 = 5

the nth term of the series is

`a_(n)` = a₁ + (n - 1)d

given a₂ = 12 , then

a₁ + d = 12 , that is

a₁ + 5 = 12 ( subtract 5 from both sides )

a₁ = 7

Then

S₃₀ =
`(30)/(2)` [ ( 2 × 7) + (29 × 5) ] = 15(14 + 145) = 15 ×159 = 2385