Homework Help: Geometric Sequences

1. Jul 30, 2009

1. The problem statement, all variables and given/known data

Hi, there are two questions that I'm quite stuck with.

1.Find the number of terms in each of these geometric sequences.

a) 1,-2,4......1024

b) 54,18,6....2/27

2. Relevant equations

ar^n-1

3. The attempt at a solution

1. a) r= -2
1x-2^n-1 ?

b) r= 2
54x2^n-1?

I'm not familiar with having negative or dividing these sequences, however I understand the basics of dealing with a problem like this that is a positive and multiplication question.

2. Jul 30, 2009

songoku

For (a):
$$U_n = ar^{n-1}$$ ; because the last term is 1024, so

$$1024 = ar^{n-1}$$

solve for n. you already have a and r

For (b) :
r is not 2. find the right r and do the same as (a)

3. Jul 30, 2009

a)1024=1x-2^n-1
1024=-2^n-1?

b) 2/27= 54x3^n-1?

4. Jul 30, 2009

Staff: Mentor

Now solve for n in each equation. You can check you answers by writing all of the terms in each sequence and counting them.

Tip: When you're writing mathematical expressions inline (as opposed to using LaTeX), use parentheses.

Instead of this--1x-2^n-1--you should write (-2)^(n - 1).
Instead of this--54x3^n-1--you should write 54 x 3^(n - 1).

Even better would be to use the exponents button that is available when you click the Go Advanced button. Your first expression would be (-2)n - 1 and the second would be 54 x 3n - 1.

5. Jul 30, 2009

songoku

r for (b) is not 3

6. Jul 31, 2009

Дьявол

$$a_n=a_1*q^{n-1}$$

So if an=1024 and a1=1 and q=-2 what is n?

Regards.

7. Jul 31, 2009