Question

How do you find `a_100` when `a_1=-30`, d=5?

Answer 1

`a_100=465`

Explanation:

Since this problem uses `d`, the common difference, we know this is an arithmetic sequence.

The general formula for an arithmetic sequence is `a_n=a_1+(n-1)d`, where `a_n` is the `n^(th)` term, `a_1` is the first term, and `d` is the common difference.

Since we already know that `a_1=-30` and `d=5`, we can substitute these values into the formula.

`a_n=a_1+(n-1)d`

`a_n=-30+(n-1)5`

To find `a_100`, substitute `100` for `n`.

`a_100=-30+(100-1)5`

Now, we can simplify.

`a_100=-30+(99)(5)`

`a_100=-30+495`

`a_100=465`