# How do you find the missing terms of the geometric sequence: 3,---,---,---,768?

Nov 8, 2015

$12$,
$48$,
$192$

#### Explanation:

In a geometric sequence you multiply by some number $r$ to get to the next term. You can think of each comma as a sign telling you to multiply by $r$.

If we call our missing terms $a , b , c$ we know that
$3 \cdot r = a$
$3 \cdot r \cdot r = b$
$3 \cdot r \cdot r \cdot r = c$
aaand
$3 \cdot r \cdot r \cdot r \cdot r = 768$
$3 \cdot {r}^{4} = 768$
${r}^{4} = \frac{768}{3}$
${r}^{4} = \frac{768}{3}$
${r}^{4} = 256$
$r = 4$
now we can find $a , b ,$and, $c$ pretty easily
$a = 12$
$b = 48$
$c = 192$