Question

What is meant by the sum of an arithmetic sequence?

Answer 1

The sum of an arithmetic sequence is a sum of a finite number of consecutive terms of an arithmetic sequence starting from `a_1` ending at `a_n`

Explanation:

In arithmetic sequence there is nothing like a sum of a (whole) sequence, because it would have to be `+oo`. On the other hand you can calculate (that is what you probably meant) a sum of `n` terms of a sequence which can be written as:

`S_1=a_1`
`S_2=a_1+a_2`
`S_3=a_1+a_2+a_3`
and so on.

In general `S_n=a_1+a_2+a_3+...+a_n`, and such sum can be calculated using formula:

`S_n=(a_1+a_n)/2*n`