Maths

A geometric series has three terms. The sum of the three terms is 42. The third term is 3.2 times the sum of the other two. What are the terms?

  1. 👍 0
  2. 👎 0
  3. 👁 239
asked by Han
  1. Let the series be
    a, ax, ax²

    "The third term is 3.2 times the sum of the other two"
    means
    ax²/(a+ax)=3.2
    cross multiply:
    ax²=3.2(a+ax)
    cancel common factor a (≠0) & multiply by 10
    10x²-32x-32=0
    =>x=4 or x= -4/5
    Reject solution where |x|<1
    x=4, or
    "The sum of the three terms is 42" means
    a(1+4+16)=42
    a=2

    So the terms are 2, 8, 32

    1. 👍 0
    2. 👎 0
  2. Thanks for your help :D

    1. 👍 0
    2. 👎 0
    posted by Han
  3. by the way did you multiply the equation by 10 to get rid of the decimal to get a whole number?

    1. 👍 0
    2. 👎 0
    posted by Han
  4. Yes, it makes life a little easier.
    I love integers! :)

    1. 👍 0
    2. 👎 0
  5. alright thanks :D

    1. 👍 0
    2. 👎 0
    posted by Han
  6. I have one last question. How did you know a=1?

    1. 👍 0
    2. 👎 0
    posted by Han
  7. like sorry for the sequence 1, 4, 16 how did you get 1?

    1. 👍 0
    2. 👎 0
    posted by Han

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27… to find the following: Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6

    asked by Gina on October 29, 2006
  2. Math....Please help I have a deadline for tonight!

    Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6

    asked by Vianna on November 4, 2006
  3. algebra

    Can someone please help me with this problem? Thanks! Evaluate the infinite geometric series: 8+4+2+1+... I thought you needed to know the number of terms to evaluate, but how do you know them if it is infinite? The limit of Sn =

    asked by Mercy on May 30, 2007
  4. CALC II

    Determine the convergence of the following series using the nth-partial sum or geometric series formula. The sum of n=1 to inifitiy 1/(9n^2+3n-2) How do I start? I'm guessing I should factor out the denominator but whats after

    asked by Ace on June 18, 2007
  5. math

    Hi. I'm having trouble with the summation of n from i=2 of ((2^n-i)(2^n)). Any help would be greatly appreciated! the way I am reading the question you have i is going from 2 to n so there will be n-1 terms using i = 2,3,4,..,n I

    asked by relle on April 24, 2007
  6. Arithmetic

    A geometric series has a positive common ratio of r. The series has a sum to infinity of 9 and the sum of the first two terms is 5. Find the first four terms of the series.

    asked by samuel on November 25, 2017
  7. arithmetic

    1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term

    asked by kartik hans on May 24, 2014
  8. arithmetic

    1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term

    asked by kartik hans on May 23, 2014
  9. math

    sorry for before it is my first time using this website and this is the real question in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 62813. How many terms are in the series?

    asked by Bob on June 3, 2013
  10. Math *URGENT

    Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 3. Determine

    asked by Aliza on December 20, 2012
  11. PreCalculus

    Determine the sum of the geometric series: p+p^2+p^3+.....+(n terms) I know how to work the formulas but I don't understand how I can find 'tn'. Thanks, -Jay I'm not sure what you mean by 'tn'. Is that t_n, t-sub-n? Let's look at

    asked by Jay M. on September 17, 2006

More Similar Questions