Question

What is the sum of the first 30 terms of this arithmetic sequence?

6, 13, 20, 27, 34, …

Answer 1

3225

Explanation:

The sum to n terms of an arithmetic sequence is

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

where a is the first term and d the common difference

here a = 6 and

d = 13 - 6 = 20 - 13 = 7, hence

`S_(30)` =
`(30)/(2)`[ (2 × 6) + (29 × 7) ]

= 15(12 + 203) = 15 × 215 = 3225