Question

find the sum of the infinite geometric series 125 + 25 + 5 + ⋯. select one: a. 156.25 b. sum does not exist. c. -31.25 d. 104.17

Explanation:

Step1: Identify first term $a_1$

$a_1 = 125$

Step2: Calculate common ratio $r$

$r = \frac{25}{125} = \frac{1}{5} = 0.2$

Step3: Check convergence condition

Since $|r| = |0.2| < 1$, the sum exists.

Step4: Apply infinite sum formula

The formula for the sum $S$ of an infinite geometric series is $S = \frac{a_1}{1 - r}$.
Substitute values:
$S = \frac{125}{1 - 0.2} = \frac{125}{0.8} = 156.25$

Answer:

A. 156.25