SOLUTION: The 2nd term of a geometric series is 80 and the sixth term is 16/125. Find the common ratio and the first term of the series. Find also the sum to infinity of the series.

Question 817201: The 2nd term of a geometric series is 80 and the sixth term is 16/125. Find the common ratio and the first term of the series. Find also the sum to infinity of the series.
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Consider the series as starting with 80
until you find the common ratio.
a1 = 80, a5 = 16/125 and n = 5
An = A2* r^5-1
16/125 = 80* r^4
Divide both sides by 80
16/10000 = r^4
Take the root 4 of 16/10000
= 2/10
= 1/5
So the common ratio is 1/5
Multiply 80 by 5
First term = 400.
....................
Sum to Infinity = a/(1 - r)
= 400/ (1 - 1/5)
=400/ 4/5
= 500
Hope this helps.
:-)
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