Geometric Sequences: Solving Homework Questions

[nomad2817]

Homework Statement

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

Homework Equations

ar^n-1

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.

 

[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)

 

[nomad2817]

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

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

 

[Mark44]

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 3^{n - 1}.

 

[songoku]

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

r for (b) is not 3

 

[Дьявол]

a_n=a_1*q^{n-1}

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

Regards.

 

[Cyosis]

Nomad you have asked this question before with a slightly different sequence. I suggest you review what you did in this thread https://www.physicsforums.com/showthread.php?t=327268 again.