SOLUTION: Please help me solve this problem: write the correct answer in the blank. Use numerals instead of words. 4,12,36,108,.... The sum of the first ___ terms in the above sequence is

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me solve this problem: write the correct answer in the blank. Use numerals instead of words. 4,12,36,108,.... The sum of the first ___ terms in the above sequence is      Log On


   

Question 1041583: Please help me solve this problem:
write the correct answer in the blank. Use numerals instead of words.
4,12,36,108,....
The sum of the first ___ terms in the above sequence is 4,372.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of a geometric series is,
S%5Bn%5D=%28a%5B1%5D%29%28%281-r%5En%29%2F%281-r%29%29
In this case, a%5B1%5D=4 and r=3.
4372=4%281-3%5En%29%2F%281-3%29
4372=-2%281-3%5En%29
1-3%5En=-2186
-3%5En=-2187
3%5En=2187
n=log%283%2C%282187%29%29
n=log%28%282187%29%29%2Flog%28%283%29%29
n=7