Question

What is the sum of the arithmetic series below 2+5+8+...+59?

Answer 1

The sum of the arithmetic series given is
2+5+8+ ... + 59

The first term is a₁ = 2
The common difference is d = 5-2 = 3
The n-th term is a₁ + (n-1)d
Therefore the last term is given by
2 + 3(n-1) = 59
3(n-1) = 57
n-1 = 19
n = 20

The sum of n terms is

`S_(n) = (n)/(2)(a_(1) + a_(n) )`

Therefore the sum of the series is

`(20)/(2)(2+59) = 610`

Answer: 610