math

the first three terms of a GP are the first, fourth and tenth terms of an AP. given that the first term is 6 and that all the terms of a GP are different, find the common ratio.

  1. 👍 0
  2. 👎 0
  3. 👁 228
  1. a = 6
    ar = a+3d
    ar^2 = a+9d
    so,
    d = (ar-a)/3

    ar^2 = a+9a(r-1)/3
    r^2 = 1+3r-3
    r^2-3r+2 = 0
    r = 1 or 2

    since the GP terms are different, r=2 and d=2 and the sequences are

    6,12,24
    6,8,10,12,14,16,18,20,22,24

    1. 👍 0
    2. 👎 0
  2. The first ,second and sixth term of an ap and the first three terms of a gp .findthe possible values of the common ratio of the gp

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. maths

    the sum of the first nine terms of an arithmetic sequence 216. The 1st, 3rd and 7th terms form the first three terms of a geometric sequence therefore find the common difference

  2. math

    The first and second terms of an exponential sequence (G.P) are respectively the first and third terms of a linear sequence (A.P). The fourth term of the linear sequence is 10 and sum of its first five terms is 60. find (a) the

  3. maths

    the sum of the first two terms of a GP is 28,but the sum of the third and fourth terms is 252.find the second term of the gp if the seventh term is 5103. please help.

  4. algebra

    The fifth term of an A.P exceeds twice the second term by 1.The tenth term exceeds twice the fourth term by 3. Find:1.the first term. 2.the common difference. 3.the sum of first twenty five terms.

  1. Government

    How many terms can a president serve according to the Constitution? a. one term b. two terms*** c. three terms d. unlimited terms

  2. arithmetic

    In an AP the first term is 2 and the sum of the first five terms is one fourth of the sum of the next five terms. Show that the 20th term is -112.

  3. Vectors Math

    1. AF in terms of AB 2. AE in terms of AB and BC 3. BC in terms of AF and EC Jhiska doesnt allow me to post urls so can you please search in "Intro to Vectors MCV4U U1A2 Assignment Question1 Support" on youtube which shows the

  4. Further mathematics

    An exponential sequence of positive terms and a linear sequence have the same first term.the sum of their first terms is 3 the sum of their second terms is 3/2,and the sum of their third terms is 6.find their fifth terms.

  1. mathematics

    The fifth ninth and sixteenth terms of a linear sequence ( ap) are consecutive terms of an exponential sequence 1 find the common difference of the linear sequence in terms of the 1st term 2 show that the 21st 37th and 65th terms

  2. medical terminology

    Your Aunt Mary has recently been diagnosed with emphysema. You are going to be attending a family function in the near future, and you think that some of your relatives will ask you the meaning of medical terms that they have

  3. Math

    1. The fourth and seventh terms of a geometric sequence are 6 and 384, respectively. What is the common ratio and the sixth term of the sequence? 2. The fifth and eight terms of a geometric sequence of real numbers are 7! and 8!

  4. 10th math

    The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of AP

You can view more similar questions or ask a new question.