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# 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

A) 2

B) 1

C) 2/3

D) 3/2

### 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: $$\frac{1}{1-\frac{1}{2}} = \frac{2}{3}$$

Explanation provided by Sarah Akin

## Discussion (4)

• Balogun Toheeb

The answer is 2 not 3/2
I suggest a recheck to it

• Esther Oluwafemi

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)
$$\cfrac{ar^2}{ar} = \cfrac{\frac{1}{4}}{-\frac{1}{2}}$$
$$r = -\frac{1}{2}$$
Then input the value of $$r$$ in one of the equ $$a = 1$$:
This gives us: $$\frac{1}{1-\frac{1}{2}} = \frac{2}{3}$$