Results 1 to 2 of 2

Thread: Geometric Progression - Finding variable to satisfy inequality

  1. #1
    Newbie
    Joined
    Aug 2018
    From
    UK
    Posts
    2

    Geometric Progression - Finding variable to satisfy inequality

    Hi everyone,

    Firstly, I hope I'm posting this in the right forum (pre-calculus isn't a term I'm familiar with.)

    I have a question about a geometric series that I'm stuck on. I've had a go at entering it here but I'm pretty hopeless at the LaTex package, so instead I've attached the question as an image. Please have a look and see if you might be able to help - I'd be really grateful.

    So far I have u1 = 108 and u2 = 72, and the sum to infinity = 324.

    It's the last bit I'm stuck on, finding the smallest value of k for which the sum of terms between k and infinity is less than 2.5. (the answer is 13)

    I tried Sk < 2.5 , re-arranged and simplified, then took logs of both sides so that the variable k wasn't a power, and rearranged to get k on it's own.

    (With Sk being the formula for the sum of "k" terms, and using 108 as the value for a/first term)

    Geometric Progression - Finding variable to satisfy inequality-gp-question.png
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Walagaster's Avatar
    Joined
    Apr 2018
    From
    Tempe, AZ
    Posts
    68
    Thanks
    28

    Re: Geometric Progression - Finding variable to satisfy inequality

    Quote Originally Posted by Bluebell View Post
    Hi everyone,

    Firstly, I hope I'm posting this in the right forum (pre-calculus isn't a term I'm familiar with.)

    I have a question about a geometric series that I'm stuck on. I've had a go at entering it here but I'm pretty hopeless at the LaTex package, so instead I've attached the question as an image. Please have a look and see if you might be able to help - I'd be really grateful.

    So far I have u1 = 108 and u2 = 72, and the sum to infinity = 324.
    Those are correct.


    It's the last bit I'm stuck on, finding the smallest value of k for which the sum of terms between k and infinity is less than 2.5. (the answer is 13)

    I tried Sk < 2.5 , re-arranged and simplified, then took logs of both sides so that the variable k wasn't a power, and rearranged to get k on it's own.

    (With Sk being the formula for the sum of "k" terms, and using 108 as the value for a/first term)

    Click image for larger version. 

Name:	GP Question.png 
Views:	8 
Size:	58.2 KB 
ID:	38883
    Without seeing your work it's hard to tell where your error is. You should be working with$$
    \sum_{n=k}^\infty 162\left( \frac 2 3\right)^k = \frac{162\left( \frac 2 3\right)^k}{\frac 1 3} = 486\left(\frac 2 3\right)^k =2.5$$
    Solving for $k$ gives $12.9972$ approximately so the answer is $13$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: Jan 4th 2018, 06:33 AM
  2. Replies: 9
    Last Post: Aug 9th 2012, 09:33 AM
  3. finding the terms of a geometric progression
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: Apr 1st 2012, 05:48 PM
  4. Geometric Progression or Geometric Series
    Posted in the Math Topics Forum
    Replies: 8
    Last Post: Oct 8th 2009, 07:31 AM
  5. Replies: 8
    Last Post: Mar 23rd 2009, 07:26 AM

/mathhelpforum @mathhelpforum