# How do you determine whether the sequence 9/4, 2, 7/4, 3/2, 5/4,... is arithmetic and if it is, what is the common difference?

Feb 17, 2017

It is an arithmetic sequence
The common difference is $- \frac{1}{4}$

#### Explanation:

So that we can make a direct comparison make all the denominators the same giving:

$\frac{9}{4} \text{; "8/4"; "7/4"; "6/4"; } \frac{5}{4}$

Observe that in each case the next term is $\frac{1}{4}$ less.

As this difference is consistent then it is an arithmetic sequence.
The common difference is $- \frac{1}{4}$. The minus sign is very important.

$\frac{8}{4} - \frac{9}{4} = - \frac{1}{4}$

$\frac{7}{4} - \frac{8}{4} = - \frac{1}{4}$

$\frac{6}{4} - \frac{7}{4} = - \frac{1}{4}$

$\frac{5}{4} - \frac{6}{4} = - \frac{1}{4}$