If the sum of a geometric series is 80, and the first term is 5, and the number of terms is 5, how can I determine the common ratio?
[Math] Finding the common ratio of a geometric series from the sum and first term
sequences-and-series
sequences-and-series
If the sum of a geometric series is 80, and the first term is 5, and the number of terms is 5, how can I determine the common ratio?
Best Answer
This is pretty much brute-force.
Let r be the common ratio. Then $5+5r+5r^2+5r^3+5r^4=80$, so $r+r^2+r^3+r^4=15$. Now just use the series formula!