Is the following a geometric sequence 1, -2, 4, -8, 16,…?

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Is the following a geometric sequence 1, -2, 4, -8, 16,…?

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Answer 1 · 2015-11-25T00:46:07

The terms listed are consistent with being a geometric sequence with initial term $1$ $1$ and common ratio $- 2$ $-2$

Explanation:

The ratio of any two successive terms listed is $- 2$ $-2$ , so this can be a geometric sequence. I say can be because we do not know what the following terms are.

For example, the same terms are given by the formula:

$a_{n} = \frac{1}{0!} - \frac{3}{1!} (n - 1) + \frac{9}{2!} (n - 1) (n - 2)$ $a_n = 1/(0!)-3/(1!)(n-1)+9/(2!)(n-1)(n-2)$

$- \frac{27}{3!} (n - 1) (n - 2) (n - 3) + \frac{81}{4!} (n - 1) (n - 2) (n - 3) (n - 4)$ $-27/(3!)(n-1)(n-2)(n-3)+81/(4!)(n-1)(n-2)(n-3)(n-4)$

but this formula would make $a_{6} = 211$ $a_6 = 211$ rather than $- 32$ $-32$

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Is the following a geometric sequence 1, -2, 4, -8, 16,…?

1 Answer

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