Question

Your Turn
Find the infinite geometric sum of -144 +24 - 4 + ...​

Answer 1

Answer:

$-123\dfrac{3}{7}$

Step-by-step explanation:

Find the infinite geometric sum of -144 +24 - 4 + ...​

The sum of infinite geometric sequence is

$S=\dfrac{b_1}{1-r},$

where $b_1$ is the first term and $r$ is the common ratio.

In your case,

$b_1=-144,\\ \\b_2=24,\\ \\b_3=-4,\\ \\r=\dfrac{b_2}{b_1}=\dfrac{24}{-144}=-\dfrac{1}{6}\\ \\ \bigskip\ \bigskip\ \bigskip =\dfrac{b_3}{b_2}=\dfrac{-4}{24}=-\dfrac{1}{6}$

So, the sum is

$S=\dfrac{-144}{1-\left(-\dfrac{1}{6}\right)}=\dfrac{-144}{1+\dfrac{1}{6}}=-\dfrac{144}{\dfrac{7}{6}}=-\dfrac{864}{7}=-123\dfrac{3}{7}$