SOLUTION: The sum of the first 30 terms of a geometric sequence is: 18[1-(2/3)^30] ___________ ____ 1/3 a. what are the first five terms of the sequence? b. Estimate the sum of th

Algebra ->  Sequences-and-series -> SOLUTION: The sum of the first 30 terms of a geometric sequence is: 18[1-(2/3)^30] ___________ ____ 1/3 a. what are the first five terms of the sequence? b. Estimate the sum of th      Log On


   

Question 1047528: The sum of the first 30 terms of a geometric sequence is:
18[1-(2/3)^30]
________________
1/3
a. what are the first five terms of the sequence?
b. Estimate the sum of the first one million terms. (How do I do this?)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
It's quite obvious from the fact S%5B30%5D=+18%2A%28%281-%282%2F3%29%5E30%29%2F%281%2F3%29%29 that
a%5B1%5D+=+18%5D and r = 2/3
a. a%5B1%5D+=+18%5D, a%5B2%5D+=+12%5D, a%5B3%5D+=+8%5D, a%5B4%5D+=+16%2F3%5D, a%5B5%5D+=+32%2F9%5D.

b. .
Since 0 < 2/3 < 1, %282%2F3%29%5E1000000%2F%281-2%2F3%29+=+3%2A%282%2F3%29%5E1000000 is practically 0.
Thus an estimate of S%5B1000000%5D is +18%2F%281-2%2F3%29+=+54.