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Is the series -2, 8, -32, 128...an arithmetic or geometric series. Is it possible to...

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xetatheta | Student, Kindergarten | Salutatorian

Posted June 8, 2011 at 2:48 AM via web

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Is the series -2, 8, -32, 128...an arithmetic or geometric series. Is it possible to find the next term?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 8, 2011 at 2:49 AM (Answer #1)

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Consider the terms of the series that are given: -2, 8, -32, 128...

8 - (-2) = 10 but -32 - 8 = -40 and 128 - (-32) = 160. As the consecutive terms do not have a common difference, this is not an arithmetic series.

8/-2 = -4, -32/8 = -4 and 128/-32 = -4. Each pair of consecutive terms has a common ratio which is -4.

We can determine the next term by multiplying 128 with -4 and we get -512

The given series is a geometric series and the next term is -512

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