Question

For the arithmetic sequence beginning with the terms {9, 14, 19, 24, 29, 34 ...}, what is the sum of the first 23 terms?

Answer 1

1472

Explanation:

The sum of n terms of an arithmetic sequence is

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

where a₁ is the first term and d the common difference

Here a₁ = 9 and d = 19 - 14 = 5 , thus

`S_(23)` =
`(23)/(2)` [ (2 × 9) + (22 × 5) ]

= 11.5 (18 + 110) = 11.5 × 128 = 1472