Question

If the sum of the first `100` terms of an arithmetic series with common difference `9` is `20888`, what is the first term?

Answer 1

The first term is `-236.62`.

Explanation:

We use the formula `s_n = n/2(2a + (n - 1)d)` to find the sum of the first `n` terms of an arithmetic series with common difference `d` and first term `a`.

`20888 = 100/2(2a + (100 - 1)9)`

Solving for `a` we obtain:

`20888 = 50(2a + 891)`

`20888 = 100a + 44550`

`-23662 = 100a`

`a = -236.62`

`:.` The first term of the series is `-236.62`.

Hopefully this helps!