arithmetic

posted by .

I have a Q that im trying to solve:
it says: the 1st , 2nd, and 3rd term of a geo. sequence is the same as the 1st, 7th and 9th terms of an arith. sequence.: I have to find the common ratio.

So i know: a+8d = a(r^2) (1)
a+6d = ar (2)

but i don't know how to solve this simulataneously! if I divide 1 with 2 i get r = (a+8d) / (a+6d) don't knwo how I should solve it.. iknow the answer is (1/3) in the book. please help.

  • arithmetic -

    ok, let's call your first result of
    r = (a+8d) / (a+6d) #1 equation

    You could also subtract the two equations to get
    ar^2 - ar = 2d
    r^2 - r = 2d/a let's call that #2

    Here is where it gets messy...
    sub #1 into #2
    (a+8d)^2/(a+6d)^2 - (a+8d)/(a+6d) = 2d/a
    finding a common denominator of (a+6d)^2 and simpifying the left side, I got
    (2ad + 16d^2)/(a+6d)^2 = 2d/a
    divide both sides by 2d

    (a+8d)/(a+6d)^2 = 1/a
    Cross-multiply and simplify to get
    a^2 + 12ad + 3d^2 = a^2 + 8ad
    36d^2 + 4ad = 0
    9d^2 + ad = 0
    d(9d + a) = 0
    d = 0 (the arithmetic sequence would not change) OR
    d = -9a
    back into #1
    r = (a+8d)/(a+6d)
    = (-9d + 8d)/(-9d + 6d)
    = -d/-3d
    = 1/3

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    The third and seventh terms of an arithmetic sequence are 10 and 20. 1) What is the value of the 1st term?
  2. Math

    first three terms of a geometric sequence are the same as the 1st, 9th and 11th terms of an arithmetic sequence, respectively. What is the common ratio in the geometric sequence ?
  3. math

    in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence …
  4. mathematics

    THE 1ST, 3RD AND 9TH TERM OF A LINEAR SEQUENCE A.P ARE THE 1ST THREE TIMES OF G.P. IF THE 7TH TERM OF THE LINEAR SEQUENCE IS 14. CALCULATE (A) 20TH TERM OF THE LINEAR SEQUENCE (B) SUM OF THE 1ST, 12TH TERM OF THE G.P
  5. math

    in an arithmetic sequence whose first term is 4, the 1st, 3rd and 7th terms form consecutive terms of geometric sequence, find the sum of the first three terms of the arithmetic sequence
  6. 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
  7. Math

    Determine whether each sequence is arithmetric or geometric. Find the next three terms. 1.14, 19, 24, 29,... geo, 34, 39, 44**** arithmetric, 32,36,41**** arithmetric, 34, 39, 44 The sequence is neither geo nor arith 2.-4,8,-16,32,... …
  8. math help fast

    Determine whether each sequence is arithmetric or geometric. Find the next three terms. 1.14, 19, 24, 29,... geo, 34, 39, 44**** arithmetric, 32,36,41**** arithmetric, 34, 39, 44 The sequence is neither geo nor arith 2.-4,8,-16,32,... …
  9. 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 ?
  10. Math

    Find the arithmetic sequence whose 1st term is 1 and the 1st, 2nd and 6th terms form a geometric sequence

More Similar Questions