SOLUTION: In a geometric series, the 9th term is equal to 8 times the 6th term, while the sum of the first five terms is 93. Find the nth term of this series and the sum of the first twenty

Algebra ->  Sequences-and-series -> SOLUTION: In a geometric series, the 9th term is equal to 8 times the 6th term, while the sum of the first five terms is 93. Find the nth term of this series and the sum of the first twenty       Log On


   

Question 1035304: In a geometric series, the 9th term is equal to 8 times the 6th term, while the sum of the first five terms is 93. Find the nth term of this series and the sum of the first twenty terms.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
It is given that a%5B9%5D+=+8a%5B6%5D <==> a%5B1%5D%2Ar%5E8+=+8%2Aa%5B1%5D%2Ar%5E5
==> r%5E3+=+8 ==> r+=+2.
Now from the other given, S%5B5%5D+=+a%5B1%5D%2A%28%281-2%5E5%29%2F%281-2%29%29+=+31a%5B1%5D+=+93
==> a%5B1%5D+=+3.
==> The general term of this geometric sequence is a%5Bn%5D+=3%2A2%5E%28n-1%29.
The sum of the first twenty terms is S%5B20%5D+=+3%2A%28%281-2%5E20%29%2F%281-2%29%29+=+3145725