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

  1. 👍 0
  2. 👎 0
  3. 👁 772
  1. just use your definitions:

    the terms would be a, ar, and ar^2

    so a(ar)(ar^2) = 343
    a^3 r^3 = 343
    (ar)^3 = 343
    ar = 7 or a = 7/r

    a + ar + ar^2 = 49/2
    a(1 + r + r^2) = 49/2
    (7/r)(1 + r + r^2) = 49/2
    7/r + 7 + 7r = 49/2
    times 2r
    14 + 14r + 14r^2 = 49r
    14r^2 - 35r + 14 = 0
    2r^2 - 5r + 2 = 0
    (2r - 1)(r - 2) = 0
    r = 1/2 or r = 2

    if r = 1/2, a = 7/(1/2) = 14
    if r = 2, a = 7/2

    state your conclusion

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    The third,sixth and seventh terms of a geometric progression(whose common ratio is neither 0 nor 1) are in arithmetic progression. Prove dat d sum of d first three is equal to d fourth term

  2. maths

    the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and 9th terms of the progression is 52. find the first term, the common difference and the sum of the first ten terms of the progression.

  3. Arithmetic

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

  4. 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

  1. math

    The sum of the 1st nine terms of an arithmetic series is 216. The 1st,3rd and the 7th terms of series form the 1st three terms of a geometric series. Find the 1st term and the constant difference of the arithmetic series ?

  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. 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. 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

  1. arithmetic progression

    An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference.

  2. Math

    If 6, p and 14 are consecutive terms in arithmetic progression(A.P) Find the value of p

  3. Math

    The sum of the 4th and 6th terms of an AP is 42. The sum of the 3rd and the 9th term of progression is 52, find the first term and the common difference of the sum of the 1st, 10th terms of the progression

  4. 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.

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