# How do you find the formula for a_n for the arithmetic sequence 4, 3/2, -1, -7/2,...?

Feb 11, 2017

If the initial term is ${a}_{0} = 4$ then ${a}_{n} = 4 - \frac{5}{2} n$
If the initial term is ${a}_{1} = 4$ then ${a}_{n} = 4 - \left(5 \cdot \left(n - 1\right)\right)$

#### Explanation:

This appears to be an arithmetic sequence (and the question was asked under the heading Arithmetic Sequences)
Checking the difference between successive terms we see that
$\textcolor{w h i t e}{\text{XXX}} {a}_{i + 1} = {a}_{i} - \frac{5}{2}$
That is the initial value is reduced by a further $\frac{5}{2}$ for each successive term.

When I learned this stuff (many years ago), the initial term was denoted ${a}_{0}$.
It seems that ${a}_{1}$ is now a more common designation for that first term (at least that is what I think I am seeing on this site)