# What is a possible value for the missing term of the geometric sequence 1250,__,50,..?

Jan 4, 2017

$\pm 250$

#### Explanation:

The general term of a geometric sequence has the form:

${a}_{n} = a \cdot {r}^{n - 1}$

where $a$ is the initial term and $r$ the common ratio.

In our example:

${a}_{1} = 1250 \text{ }$ and $\text{ } {a}_{3} = 50$

So:

${r}^{2} = \frac{a {r}^{2}}{a {r}^{0}} = {a}_{3} / {a}_{1} = \frac{50}{1250} = \frac{1}{25} = \frac{1}{5} ^ 2$

Hence:

$r = \pm \frac{1}{5}$

Then:

${a}_{2} = a \cdot {r}^{2 - 1} = 1250 \cdot \left(\pm \frac{1}{5}\right) = \pm 250$