Question

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

Answer 1

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(n)=a((1-r^n)/(1-r))`
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!