Results 1 to 2 of 2

Math Help - Geometric sequence

  1. #1
    Newbie
    Joined
    Jan 2009
    From
    San Fran!
    Posts
    6

    Geometric sequence

    In a geometric sequence, t1 + t2 + t3 = 21 and t4 + t5 + t6 =168. Find the sequence.

    how do u use the formula Sn = a(r^n -1)/r -1) to find the sequence?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,864
    Thanks
    744
    Hellp, megs_world!

    In a geometric sequence: . t_1 + t_2 + t_3 \:=\: 21\,\text{ and }\,t_4 + t_5 + t_6 \:=\:168

    Find the sequence.

    how do u use the formula: S_n \:=\: a\frac{r^n -1}{r -1} to find the sequence?

    We know the sum of the first 3 terms: . S_3 \:=\:21
    . . Hence: . a\frac{r^3-1}{r-1} \:=\: 21 .[1]

    We know the sum of the first 6 terms: . (t_1+t_2+t_3) + (t_4+t_5+t_6) \:=\:21 + 168 \:=\:189
    . . Hence: . a\frac{r^6-1}{r-1} \:=\:189 .[2]

    Divide [2] by [1]: . \frac{a\dfrac{r^6-1}{r-1}}{a\dfrac{r^3-1}{r-1}} \:=\:\frac{189}{21} \quad\Rightarrow\quad \frac{r^6-1}{r^3-1} \:=\:9

    Factor and reduce: . \frac{(r^3-1)(r^3+1)}{r^3-1} \:=\:9 \quad\Rightarrow\quad r^3 + 1 \:=\:9

    . . Then: . r^3 \:=\:8 \quad\Rightarrow\quad\boxed{ r \:=\:2}

    Substitute into [1]: . a\frac{2^3-1}{2-1} \:=\:21 \quad\Rightarrow\quad7a \:=\:21 \quad\Rightarrow\quad\boxed{ a \:=\:3}


    Therefore, the sequence is: . t_n \:=\:3\cdot2^{n-1} \quad\Rightarrow\quad 3, 6, 12, 24, 48, 96\hdots

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Geometric Sequence
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 23rd 2008, 06:42 PM
  2. geometric Sequence
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 20th 2008, 07:20 AM
  3. Geometric sequence
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 18th 2007, 05:39 AM
  4. Replies: 2
    Last Post: January 23rd 2007, 09:47 AM
  5. Replies: 12
    Last Post: November 15th 2006, 01:51 PM

Search Tags


/mathhelpforum @mathhelpforum