Find the common ratio r for the given infinite geometric sequence.
-A town has a population of 10,000 people and is increasing by 10% every year. What will the 175) population be at the end of 4 years?
A) 13,310 people
B) 4641 people
C) 14,641 people
D) 14,000 people

Question

Quizplus · Accepted Answer

The common ratio $r$ for the given geometric sequence is 1.10, as the population increases by 10% each year. To find the population at the end of 4 years, use the formula for the $n$th term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$, where $a_1 = 10,000$, $r = 1.10$, and $n = 4$. Thus, $a_4 = 10,000 \cdot (1.10)^3 = 10,000 \cdot 1.331 = 13,310$. However, the correct calculation should be $a_4 = 10,000 \cdot (1.10)^4 = 10,000 \cdot 1.4641 = 14,641$ people, indicating a mistake in the initial explanation but the correct choice is identified based on the correct calculation.

Find the Common Ratio R for the Given Infinite Geometric