Question

The sum of an infinite geometric series is three times the first term. Find the common ratio of this series.

Answer 1

Answer:

$\frac{2}{3}$

Step-by-step explanation:

The sum of an  infinite geometric series is expressed according to the formula;

$S_\infty = \dfrac{a}{1-r}$ where;

a is the first term of the series

r is the common ratio

If the sum of an infinite geometric series is three times the first term, this is expressed as $S_\infty = 3a$

Substitute $S_\infty = 3a$ into the formula above to get the common ratio r;

$3a = \dfrac{a}{1-r}$

$cross \ multiply\\\\3a(1-r) = a\\\\3(1-r) = 1$

open the parenthesis

$3 - 3r = 1$

subtract 3 from both sides

$3 - 3r -3= 1-3\\\\-3r = -2\\\\r = \frac{2}{3}$

Hence the common ratio of this series is $\frac{2}{3}$