**The second term of an infinite geometric series is -1/2 and the third term is 1/4....**

### Question

The second term of an infinite geometric series is -1/2 and the third term is 1/4. The sum of the series is### Options

A) 2

B) 1

C) 2/3

D) 3/2

The correct answer is C.

### Explanation:

F = \(\cfrac{a}{1-r}\), \(a=?, r=?\)

To find sum to infinity, \(a\) and \(r\) are required:

\(ar = -\frac{1}{2}\)...(1)

\(ar^2 = \frac{1}{4}\)...(2)

Divide equ 2 by 1:

\(\cfrac{ar^2}{ar} = \cfrac{\frac{1}{4}}{-\frac{1}{2}}\)

\(r = -\frac{1}{2}\)

Then input the value of \(r\) in one of the equ \(a = 1\):

This gives us: \(\frac{1}{1-\frac{1}{2}} = \frac{2}{3}\)

To find sum to infinity, \(a\) and \(r\) are required:

\(ar = -\frac{1}{2}\)...(1)

\(ar^2 = \frac{1}{4}\)...(2)

Divide equ 2 by 1:

\(\cfrac{ar^2}{ar} = \cfrac{\frac{1}{4}}{-\frac{1}{2}}\)

\(r = -\frac{1}{2}\)

Then input the value of \(r\) in one of the equ \(a = 1\):

This gives us: \(\frac{1}{1-\frac{1}{2}} = \frac{2}{3}\)

Explanation provided by Sarah Akin

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## Discussion (4)

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The answer is 2 not 3/2

I suggest a recheck to it

(B) is the answer.

The formula for sun to infinity contains minusvin the denominator already i.e 1-r. Therefore when minuus is brought into the formula it becomes positive giving us 1 as the answer.

F = \(\cfrac{a}{1-r}\), \(a=?, r=?\)

To find sum to infinity, \(a\) and \(r\) are required:

\(ar = -\frac{1}{2}\)...(1)

\(ar^2 = \frac{1}{4}\)...(2)

Divide equ 2 by 1:

\(\cfrac{ar^2}{ar} = \cfrac{\frac{1}{4}}{-\frac{1}{2}}\)

\(r = -\frac{1}{2}\)

Then input the value of \(r\) in one of the equ \(a = 1\):

This gives us: \(\frac{1}{1-\frac{1}{2}} = \frac{2}{3}\)

The answer should be 2 not ⅔