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Geometric Sequences

  1. Jul 30, 2009 #1
    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. jcsd
  3. Jul 30, 2009 #2
    For (a):
    [tex]U_n = ar^{n-1}[/tex] ; because the last term is 1024, so

    [tex]1024 = ar^{n-1}[/tex]

    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)
     
  4. Jul 30, 2009 #3
    a)1024=1x-2^n-1
    1024=-2^n-1?

    b) 2/27= 54x3^n-1?
     
  5. Jul 30, 2009 #4

    Mark44

    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.
     
  6. Jul 30, 2009 #5
    r for (b) is not 3
     
  7. Jul 31, 2009 #6
    [tex]a_n=a_1*q^{n-1}[/tex]

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

    Regards.
     
  8. Jul 31, 2009 #7

    Cyosis

    User Avatar
    Homework Helper

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