# What is the nth term of the arithmetic sequence 7, 5, 3, 1,...?

Dec 3, 2014

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. ${a}_{n} = {a}_{1} + d \left(n - 1\right)$

If we want the first term we use the $7$ as ${a}_{1}$, and we get ${a}_{n} = 7 - 2 \left(1 - 1\right)$ which gives $7$.

If we want to find the second term, we use the $7$ again for ${a}_{1}$ and we get ${a}_{n} = 7 - 2 \left(2 - 1\right)$.

Notice how the $n$ is the number of the term we want and, therefore, is how we find the ${n}^{t h}$ term.