What is the sum of the first ten terms in the geometric series 4 - 12 + 36 - 108 + ... ?

This is a geometric

first term is a = 4

2nd term is mult by 3 to give us 4 (31)

3rd term is 4 (32)

4rth term is 4 (33)

and the 12th term is 4 (311)

so a is 4 and the common ratio (r) is equal to 3

that's all you need to know.

The formula for the sum of the 12 terms in geometric is:

S (n) = a (1-rn1-r)

substituting a=4 and r=3, we get:

s (12) = 4 (1-3121-3) 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 (1-341-3)

All you have to do is figure out what the first term is and then figure out the common ratio between them!