Question

What is the sum of the arithmetic sequence `2, 4, 6, ..., 1880` ?

Answer 1

`884540`

Explanation:

The sum of an arithmetic sequence is the number of terms multiplied by the average term and the average term is the same as the average of the first and last terms.

In our example we can see that the number of terms is `940` by separating out a factor of `2`, so:

`2+4+6+...+1880 = 2 * (1+2+3+...+940)`

`color(white)(2+4+6+...+1880) = 2 * 940 * (1+940)/2`

`color(white)(2+4+6+...+1880) = 940 * 941`

`color(white)(2+4+6+...+1880) = 884540`

Answer 2

`884540`
Use a sigma sum series.

Explanation:

The pattern is `n*2`, for every n (some number) there is a two added to it.
For example:
`0*2=0`
`1*2=2`
`2*2=4` etc.
If `sum_(i=1)=n*2`
which computes to be `884540`
So if you do the amount of terms `n` and square by two (because the anti derivative of `2n` is `n^2`) and add `940` you get your answer. `int2n=n^2+c` and `c=940` because it is your amount of terms.
I remember it using calculus based integration, I am not sure what they taught you in Precalculus.