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.

  1. 👍
  2. 👎
  3. 👁
  1. a + ar = 28
    ar^2 + ar^3 = 252

    a(1+r) = 28
    ar^2(1+r) = 252

    ar^2(1+r)/a(1+r) = r^2 = 252/28 = 9
    r = 3 or -3

    a(1-3) = 28 ==> a = -14
    a(1+3) = 28 ==> a = 7

    So, now we need to know that

    ar^6 = 5103
    7*3^6 = 5103
    Unfortunately, that works whether r is 3 or -3

    Using r = -3

    7+(-21) = -14
    7+21 = 28

    So, r=3

    7r = 21

    The bit about the 7th term is redundant and unhelpful.

    1. 👍
    2. 👎
  2. Thanks for the solution

    1. 👍
    2. 👎
  3. Thanks 4 d answer

    1. 👍
    2. 👎
  4. Thanks for the reasonable solution

    1. 👍
    2. 👎
  5. Nice one

    1. 👍
    2. 👎
  6. How can I get the second term of the gp if the seventh term is 5103

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    5. In a geometric sequence, the sum of the first five terms is 44 and the sum of the next five terms is -11/8. Find the common ratio and first term of the series.

  2. math

    The sum of the first 20 terms of an arithmetic series is identical to the sum of the first 22 terms. If the common difference is -2, find the first term.

  3. mathematics

    1} the first term of an AP is 2 and the common difference is 3.Find the sum of the first 11 terms. 2}The 2nd and 5th terms of a GP are -6 and 48 respectively.Find the sum of the first four terms

  4. 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

  1. Geometric series

    The sum of the first five terms of a geometric series is 186 and the sum of the first six terms is 378. if the fourth term is 48, determine a(first term),r(ratio), t10, S10.

  2. Math

    In an arithmetic series, the sum of the 5th to the 8th terms inclusive is 114, whilst the sum of the 12th to 15th terms inclusive is 198. What is the 21st term? I have got 99=2a +3d and 57= 2a+3d Im not sure what to do now

  3. maths

    the sum of 3rd and 5th terms of an a.p is 38 and sum of 7th and 10th terms of an a.p is 83,find the a.p. please help all questions please help please.

  4. 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.

  1. Mathematics

    The sum of the 1st and 2nd terms of an AP is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms

  2. Math

    The sum of 16 terms of an AP is -504,while the sum of its 9 terms is -126.find the sum of its 30 terms

  3. Math

    The sum of the first 21 terms of a linear sequence is 28 and the sum of the first 28 terms is 21 . find which term of the sequence is 0 and also the sum of the terms preceeding it

  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.

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