# Whats the missing term in the geometric sequence 2, __, 50?

Nov 7, 2015

$10$

#### Explanation:

In a geometric sequence you multiply by some number $r$ to get to the next term. So if we call our missing term $x$ we know this:
$2 \cdot r = x$
$x \cdot r = 50$

substitute...
$2 \cdot r \cdot r = 50$

You could also think of each step in the sequence as multiplying by another $r$, so basically your first term times $r$ and times $r$ again gives you 50. or $2 {r}^{2} = 50$

Either way will get you there.
solve for r...
$2 {r}^{2} = 50$
${r}^{2} = 25$
$r = 5$
Not done just yet...
plug in $r$ into one of the above equations...
$2 \cdot r = x$
$2 \cdot 5 = x$
$10 = x$