# [SOLVED] Geometric Sequence

• February 2nd 2009, 01:39 PM
nikie1o2
[SOLVED] Geometric Sequence
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!!
• February 2nd 2009, 01:55 PM
Plato
$\sum\limits_k {\left( { - 1} \right)^{k + 1} x^{2k - 1} }$
• February 2nd 2009, 01:58 PM
nikie1o2
Im sorry, I should have mentioned the sequence starts at 0 not 1. Would that answer still apply to the sequence?(Doh)
• February 2nd 2009, 02:09 PM
Soroban
Hello, nikie1o2!

Quote:

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

• February 2nd 2009, 03:15 PM
Plato
Quote:

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?(Doh)

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