[SOLVED] Geometric Sequence

**nikie1o2** · February 2nd 2009, 12:39 PM

Im working on putting sequences in formulas. I have the sequence:
X-X^3+X^5-X^7+X^9+....

I see the difference in exponets is Plus 2, but how do I get the negative and positive terms?

Thanks 4 Any help!!

**Plato** · February 2nd 2009, 12:55 PM

$\sum\limits_k {\left( { - 1} \right)^{k + 1} x^{2k - 1} }$

**nikie1o2** · February 2nd 2009, 12:58 PM

Im sorry, I should have mentioned the sequence starts at 0 not 1. Would that answer still apply to the sequence?

**Soroban** · February 2nd 2009, 01:09 PM

Hello, nikie1o2!

I'm working on putting sequences in formulas. . not sure what this means

I have the sequence: . $x-x^3+x^5-x^7+x^9+\hdots$

I see the difference in exponents is Plus 2,
but how do I get the negative and positive terms?

If you are working with Geometric Series, then you want to identify
. . the first term $a$ , and the common ratio, $r.$

In this problem, the first term is $x$ , the common ratio is $\text{-}x^2$

If you are trying to write the general term for the series, $a_n$ ,

. . it looks like this: . $a_n \:=\:(\text{-}1)^{n+1}x^{2n-1}$

**Plato** · February 2nd 2009, 02:15 PM

Originally Posted by nikie1o2

Im sorry, I should have mentioned the sequence starts at 0 not 1. Would that answer still apply to the sequence?

It does make a slight different.
$a_n=(-1)^n x^{2n+1}$

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