Question

What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

Answer 1

For the regular sequence 1, 2, 3, ...,
`n`, then sum is

`(n(n+1))/(2)`

If we multiply each number by 7 (7, 14, 21, ...), then the sum is

`(7n(n+1))/(2)`
and if we add 1 to each number (8, 15, 22, ...) then the sum is

`(7n(n+1))/(2)+n`

We have
`n=26` terms, so the sum is:

`(7(26)(27))/(2)+26`

`=7(13)(27)+26`

`=91(27)+26`

`=2457+26`

`=2483`