# How do you tell whether the sequence 3, 5, 7, 9, 11,... is geometric?

Feb 23, 2017

It is not geometric.
${a}_{n} = 2 n + 1$

#### Explanation:

Since in a geometric sequence each term after the first is found by multiplying the previous one by a fixed, non-zero number, thus we have to get that number by dividing nth term by the previous term.

We can say a sequence is geometric if and only if all of the division answers are fixed and constant.

$\setminus \frac{5}{3} \setminus \ne \setminus \frac{7}{5}$ so your sequence is not geometric.