Question

What is the sum of the arithmetic series below 2+5+8+...+56​

Answer 1

551

Explanation:

The sum to n terms of an arithmetic sequence is

`S_(n)` =
`(n)/(2)`( first + last)

The number of terms is

`a_(n)` = a + (n - 1)d ← d is the common difference, a is the first term

d = 5 - 2 = 8 - 5 = 3, hence

2 + 3(n - 1) = 56

2 + 3n - 3 = 56

3n - 1 = 56 ⇒ 3n = 57 ⇒ n = 19

`S_(19)` =
`(19)/(2)` ( 2 + 56 ) = 19 × 29 = 551