Find the common ratio r for the given infinite geometric sequence.
-The beginning population of a small town was 13,000 people. Due to decline in industrial growth the population has since been decreasing at a rate of 5% every year. What was the population of
This town 10 years later?
A) 7784 people
B) 6292 people
C) 7002 people
D) 8643 people

Question

Quizplus · Accepted Answer

The common ratio $r$ for the given geometric sequence is $1 - 0.05 = 0.95$, since the population decreases by 5% each year. To find the population 10 years later, we use the formula for the $n$th term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$, where $a_1 = 13000$, $r = 0.95$, and $n = 11$ (since we start counting from year 0 for the initial population). Thus, $a_{11} = 13000 \cdot 0.95^{10} \approx 7784$ people.

Find the Common Ratio R for the Given Infinite Geometric