SOLUTION: This is a question on my study guide for my test and I don't know how to solve this. If I can't figure this out, then I might fail my test. Please help me! I would greatly apprecia

Algebra ->  Sequences-and-series -> SOLUTION: This is a question on my study guide for my test and I don't know how to solve this. If I can't figure this out, then I might fail my test. Please help me! I would greatly apprecia      Log On


   

Question 856103: This is a question on my study guide for my test and I don't know how to solve this. If I can't figure this out, then I might fail my test. Please help me! I would greatly appreciate it.
The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 36 and the common ratio is 1/2. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

a1 = 36 and r = 1/2= .5

a%5Bn%5D+=+36%28.5%29%5E%28n-1%29  |.5| < 1

sum%28+a%5Bn%5D%2Cn=1%2C+infinity+%29 = a%5B1%5D%2F%281-r%29

sum%28+36%28.5%29%5E%28n-1%29%2Cn=1%2C+infinity+%29 = 36%2F%281%2F2%29 = 72

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of an infinite geometric series is equal to a1 / (1-r).
r = 1/2
a1 = 36
sum is equal to 36 / (1 - 1/2) which is equal to 36/(1/2) which is equal to 72.
that's your answer.
the formula for the sum of a geometric series is normally shown as:
Sn = A1 / (1-r)
A1 is the first term in the sequence.
Sn is the sum of all the terms.
the following link discusses geometric series:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54d_geom.htm
if you are not familiar with how they work, this is a good review.
scroll down about 3/4 of the way down the page to get to sum of an infinite geometric series.