Question

Find the sum of the first 41 terms of the following series, to the nearest integer.

12, 19, 26, ...

Answer 1

The sum of the first 41 terms is 6232

Explanation:

The sequence is an arithmetic progression with:

`a = 12` -- first term

`d = 7` --- common difference (this is calculated by 19 - 12 or 26 -19)

Required

The sum of the first 41 terms

This is calculated as:

`S_n = (n)/(2)(2a + (n-1)*d)`

In this case:
`n = 41`

So:

`S_(41) = (41)/(2)(2*12 + (41-1)*7)`

`S_(41)= (41)/(2)*304`

`S_(41) = 6232`