Results 1 to 3 of 3

Math Help - Arithmatic and Geometric Sequences Help Please?

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    19

    Arithmatic and Geometric Sequences Help Please?

    The first, second and eleventh terms of an arithmetic sequence with a common difference of 4 are the first, third and fifth terms of a geometric sequence. Find the sequence rule for the geometric and arithmetic sequences.

    Thank you for any help!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by anonymous_maths View Post
    The first, second and eleventh terms of an arithmetic sequence with a common difference of 4 are the first, third and fifth terms of a geometric sequence. Find the sequence rule for the geometric and arithmetic sequences.

    Thank you for any help!!
    Let the arithmetic series be a_n = a_1 + 4(n - 1).

    since the first terms of each sequence are the same, we know that the geometric sequence is of the form b_n = a_1r^{n - 1} (the same a_1)

    this is for n = 1,2,3, \cdots

    hence, from the arithmetic sequence we have

    a_2 = a_1 + 4

    a_{11} = a_1 + 40

    from the geometric series we know that

    b_3 = a_1r^2

    b_5 = a_1r^4


    now, know that a_1 = b_1, ~a_2 = b_3,~ a_{11} = b_5 you will be able to set up a system of equations to solve for a_1, and hence answer the problem.

    (i hope you know the formulas for an arithmetic sequence and geometric sequence to know how i got the expressions for a_n and b_n
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288
    In A.P:1st term=a, 2nd term=a+4,11th term=a+40

    In G.P. 1st term=a, 3rd term=ar^2, 5th term=ar^4

    Hence, ar^2=a+4...(1)
    ar^4=a+40...(2)

    From (1): r^2=\frac{a+4}{a}
    Into (2): a(\frac{a+4}{a})^2=a+40
    a^2+8a+16=a^2+40
    a=0.5

    If a=0.5\rightarrow0.5r^2=4.5
    r=3

    I'm not sure what you mean by sequence rule, but I've calculated the original term and ratio for the G.P, so I'm not what else you need.
    A.P.: 0.5+4k
    G.P.:  0.5(3)^k
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sum of a part arithmatic and part geometric sequence
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 25th 2009, 11:53 PM
  2. Geometric/Arithmatic Series
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 7th 2009, 06:27 AM
  3. geometric sequences (please help)
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 6th 2008, 12:32 PM
  4. Replies: 5
    Last Post: January 16th 2008, 05:51 PM
  5. geometric sequences
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 5th 2007, 01:32 PM

Search Tags


/mathhelpforum @mathhelpforum