Question

What is the `n`th term of the arithmetic sequence 7, 5, 3, 1,...?

Answer 1

This is an arithmetic sequence since there is a common difference between each term.

In this case, adding `-2` to the previous term in the sequence gives the next term.

This is the formula of an arithmetic sequence. `a_n=a_1+d(n-1)`

If we want the first term we use the `7` as `a_1`, and we get `a_n=7-2(1-1)` which gives `7`.

If we want to find the second term, we use the `7` again for `a_1` and we get `a_n=7-2(2-1)`.

Notice how the `n` is the number of the term we want and, therefore, is how we find the `n^(th)` term.