# How do you find the sum of the first 12 terms of 4 + 12 + 36 + 108 + ?

Mar 18, 2016

this is a geometric
first term is a = 4
2nd term is mult by 3 to give us 4( ${3}^{1}$)
3rd term is 4( ${3}^{2}$)
4rth term is 4( ${3}^{3}$)
and the 12th term is 4( ${3}^{11}$)

so a is 4 and the common ratio (r) is equal to 3
that's all you need to know.
oh, yeah, the formula for the sum of the 12 terms in geometric is

$S \left(n\right) = a \left(\frac{1 - {r}^{n}}{1 - r}\right)$
substituting a=4 and r=3, we get:
$s \left(12\right) = 4 \left(\frac{1 - {3}^{12}}{1 - 3}\right)$ or a total sum of 1,062,880.

you can confirm this formula is true by calculating the sum of the first 4 terms and comparing $s \left(4\right) = 4 \left(\frac{1 - {3}^{4}}{1 - 3}\right)$

works like a charm. All you have to do is figure out what the first term is and then figure out the common ratio between them!