Homework Help: Things to expect with grade 10 Geometric Sequences

1. Jun 6, 2006

wScott

We're going to be starting them in a day or two, and I just wanted to know ahead of time what you guys might think we'll be learning with them, like formulae and that kind of stuff..

2. Jun 6, 2006

HallsofIvy

There's not a whole lot you have to know about "geometric sequences". A geometric sequence is one in which you go from one number to the next by always multiplying by the same thing.

Example: 3, 6, 12, 24, 48, 96,.... The point is that 6/3= 2, 12/6= 2, 48/24= 2, 96/48= 2. In other words, you start with the number 3 and proceed to just keep multiplying by 2. If we start counting terms with n= 0 (some people start with n= 1) then the "nth" term is 3(2)n or, in more general terms, arn where a is the first term and a is the "common multiplier"j. If you start counting with n= 1, then the nth term is arn-1:you have to subtract 1 to get back to 0.

Another nice property is this: suppose we add the terms (a geometric series rather than sequenc). For example if S= a+ ar+ ar2+ ar3, then S= a+ r(a+ ar+ ar2) where we've just lost one power. Okay, put it back in: S= a+ r(a+ ar+ ar2+ ar3- ar3. See how I added and subtracted the same thing? Now separate those: S= a+ r(a+ ar+ ar2+ ar3)+ ar4= a+ r(S)+ ar4 so
S- rS= S(1-r)= a+ ar4= a(1- r4). That is,
S(1-r)= a(1- r4) so S= a (1-r4)/(1- r).

More generally, the sum of the first n terms of a geometric sequence is
Sn= a(1-rn+1)/(1- r).

3. Jun 6, 2006

wScott

Well, it seems pretty simple to me, especially after the few arithmatic formulae we've learned over the past few days. Should be fun :)