1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Geometric Sequences and Series

  1. Aug 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Q.: The sum of the first five terms of a geometric series is 5 and the sum of the next five terms is 1215. Find the common ratio of this series.

    2. Relevant equations

    Sn = [itex]\frac{a(r^n - 1)}{r - 1}[/itex]

    3. The attempt at a solution

    a + ar + ar^2 + ar^3 + ar^4 = 5
    ar^5 + ar^6 + ar^7 + ar^8 + ar^9 = 1215

    ar^5 + ar^6 + ar^7 + ar^8 + ar^9 = 1215
    -(a + ar + ar^2 + ar^3 + ar^4) = 5
    r^5 + r^5 + r^5 + r^5 + r^5 = 1210

    5r^5 = 1210
    r^5 = 242
    r = [itex]\sqrt[5]{242}[/itex]
    r [itex]\approx[/itex] 3

    Answer: From text book: 3

    Please note that [itex]\sqrt[5]{243}[/itex] is exactly 3. My answer is close but still off the mark. Can someone help me figure out how to fix this? Thank you.
     
  2. jcsd
  3. Aug 21, 2011 #2

    dynamicsolo

    User Avatar
    Homework Helper

    What if you factor r5 from your equation for 1215 and then divide it by the other equation? (Your approach is not algebraically correct.)
     
  4. Aug 21, 2011 #3
    Ok, here it is...

    r^5(a + ar + ar^2 + ar^3 + ar^4) = 1215
    a + ar + ar^2 + ar^3 ar^4 = 5

    r^5 = [itex]\frac{1215}{5}[/itex]

    r^5 = 243
    r = [itex]\sqrt[5]{243}[/itex]
    r = 3

    That works out. Thank you very much.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Geometric Sequences and Series
  1. Geometric Series (Replies: 4)

  2. Geometric series (Replies: 5)

  3. Series (Geometric?) (Replies: 5)

Loading...