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

1 Answer
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

substituting a=4 and r=3, we get:
#s(12)=4((1-3^12)/(1-3))# 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(4)=4((1-3^4)/(1-3))#

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!