Question

What is the sum of the arithmetic series 2 + 5 + 8 + ... + 53?

Answer 1

First, we must find the number of terms, n.

Explanation:

`t_n = a + (n - 1)d`

`53 = 2 + (n - 1)3`

`53 = 2 + 3n - 3`

`54 = 3n`

`18 = n`

Now that we know the number of terms we can use the formula `s_n = n/2(t_1 + t_n)`

`s_18 = 18/2(2 + 53)`

`s_18= 9(55)`

`s_18 = 495`

The sum is of 495.

When finding the sum of an arithmetic series, there are two formulas that you may use: the one presented above and `s_n = n/2{2a + (n - 1)d}`. You use the latter when you don't know the last term.

Practice exercises:

1. Find the sum of the following series: `5, 11, 17, ..., 131`

2. Find the sum of a series with the following characteristics.

3. First three terms: `7, -1, -9, ...`

4. `n = 33`

Hopefully this helps!