Question

Find the sum of the first 45 terms of the following series, to the nearest integer. 2,11, 20, ...​

Answer 1

`S_(45)` = 9000

Explanation:

there is a common difference between consecutive terms , that is

11 - 2 = 20 - 11 = 9

this indicates the sequence is arithmetic with nth term

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

where a₁ is the first term and d the common difference

here a₁ = 2 and d = 9 , then

`S_(45)` =
`(45)/(2)` [ (2 × 2) + (44 × 9) ]

= 22.5(4 + 396)

= 22.5 × 400

= 9000