Arithmetic

The sum of three consecutive terms of a geometric progression is 42, and their product is 512. Find the three terms.

  1. 👍
  2. 👎
  3. 👁
  1. use your definitions:
    "The sum of three consecutive terms of a geometric progression is 42"
    ----> a + ar + ar^2 = 42
    a(1 + r + r^2) = 42 **

    "their product is 512" --- a(ar)(ar)^2 = 512
    a^3 r^3 = 512
    (ar)^3 = 8^3
    ar = 8 ***

    divide ** by ***
    (1+r + r^2)/r = 42/8 = 21/4
    4r^2 + 4r + 4 = 21r
    4r^2 - 17r + 4 = 0
    (4r - 1)(r - 4) = 0
    r = 1/4 or r = 4

    if r = 4, in ar= 8 , a = 2
    the 3 terms are 2, 8, and 32
    check: sum = 2+8+32 = 42 ⩗
    product = 2 x 8 x 32 = 512 ⩗

    I will leave it up to you to find the other case.

    1. 👍
    2. 👎
  2. Thank you so much for your help,it helps to clear some confusions😃😃

    1. 👍
    2. 👎
  3. Good method of solving

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Three numbers form a geometric progression. If 4 is subtracted from the third term, then the three numbers will form an arithmetic progression. If, after this, 1 is subtracted from the second and third terms of the progression,

  2. MATH

    three consecutive terms of a geomentric progression series have product 343 and sum 49/2. fine the numbers. HOW WILL ONE SOLVE THAT? THANKS

  3. Maths

    a geometric progression has the second term as 9 and the fourth term as 81. find the sum of the first four terms.?

  4. Algebra 2

    In an infinite geometric progression with positive terms and with a common ratio |r|

  1. Math

    The common ratio of a geometric progression is 1/2 , the fifth term is 1/80 , and the sum of all of its terms is 127/320 . Find the number of terms in the progression.

  2. Arithmetic

    The first, second and third terms of a geometric progression are 2k+3, k+6 and k, respectively. Given that all the terms of geometric progression are positive, calculate (a) the value of the constant k (b) the sum to infinity of

  3. Maths

    The numbers p,10 and q are 3 consecutive terms of an arithmetic progression .the numbers p,6 and q are 3 consecutive terms of a geometric progression .by first forming two equations in p and q show that p^2-20p+36=0 Hence find the

  4. Math

    Find the sum to 5 terms of the geometric progression whose first term is 54 and fourth term is 2.

  1. algebra

    Find four consecutive terms in A.P whose sum is 72 and the ratio of product of the extreme terms to the product of means is 9:10

  2. Math, Series

    Given that 1/(y-x), 1/2y, and 1/y-z are consecutive terms of an arithmetic progression, prove that x,y, and z are consecutive terms of a geometric progression.

  3. math

    if k+1,2k-1,3k+1 are three consecutive terms of a geometric progression,find the possible values of the common ratio

  4. Maths

    A Geometric progression X has a first term of 4a and its sixth term is 256. Another Geometric progression Y has a first term of 3a and its fifth term is 48. Find the: (i) First term of X (ii) Sum of the first four terms of X

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