# How do you find the sum of the first 5 terms of the geometric series: 4+ 16 + 64…?

Dec 29, 2015

$1364$

#### Explanation:

${a}_{2} / {a}_{1} = \frac{16}{4} = 4$
${a}_{3} / {a}_{2} = \frac{64}{16} = 4$

$\implies$ common ratio$= r = 4$ and ${a}_{1} = 4$

Sum of a geometric series is given by
$S u m = S = \frac{a \left(1 - {r}^{n}\right)}{1 - r}$

Where $a$ is the first term $r$ is the common ratio and $n$ is the number of terms.

Sum=S=(4(1-4^5))/(1-4)=(4(1-1024))/(-3)=(4(-1023))/(-3)=(-4092)/(-3)=1364

Hence the required sum is $1364$.