Question

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

Answer 1

`-123(3)/(7)`

Explanation:

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

The sum of infinite geometric sequence is

`S=(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=(b_2)/(b_1)=(24)/(-144)=-(1)/(6)\\ \\ \bigskip\ \bigskip\ \bigskip =(b_3)/(b_2)=(-4)/(24)=-(1)/(6)`

So, the sum is

`S=(-144)/(1-\left(-(1)/(6)\right))=(-144)/(1+(1)/(6))=-(144)/((7)/(6))=-(864)/(7)=-123(3)/(7)`