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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

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

Explanation provided by Sarah Akin


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Discussion (4)

  • Balogun Toheeb

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

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  • Esther Oluwafemi

    (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.

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  • 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: \(\frac{1}{1-\frac{1}{2}} = \frac{2}{3}\)

    1. The answer should be 2 not ⅔