Maths

An arithmetic and a geometric sequence have the same first terms.(2)....and the same second term say X..The sum of the first 3 terms of the arithmetic sequence equals to the third term of the geometric sequence.Calculate the first 3 terms of each sequences

  1. 0
asked by Lucas
  1. a+d = ar
    3/2 (2a+2d) = ar^2
    3a+3d = ar^2
    3(a+d) = ar^2
    3ar = ar^2
    3r = r^2
    r = 3

    So,
    a+d = 3a
    d = 2a

    The sequences are thus
    a,3a,5a,7a,9a,...
    a,3a,9a,27a,...
    Note that a+3a+5a = 9a, as required

    Pick a value for a, and plug and chug.

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Determine whether each sequence is arithmetic or geometric. Find the next three terms. 1. 14, 19, 24, 29, . . . (1 point) geometric, 34, 39, 44 arithmetic, 32, 36, 41 arithmetic, 34, 39, 44 *** The sequence is neither geometric
  2. Math Help!!!

    determine whether each sequence is arithmetic or geometric. find the next three terms. 1. 14,19,24,29.... geometric, 34,39,44 arithmetic,32,36,41 arithmetic 34,39,44**** the sequence is nether geometric nor arithmetic 2.
  3. Maths

    1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression
  4. 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
  5. math...

    how can I tell if a sequences is airthmetic, geometric or neither? determine the first three terms of each and determine if each are airthmetic, geometric or neither. 1) tn=5t n-1+ 3 wheret 1=2 first three terms: 3,13,23
  6. algebra

    can you check my answers please? What are the first three terms of the sequence: a1 = 3 and an = 2(an1)2? 2, 8, 18 3, 18, 648 --3, 32, 50 2, 6, 12, 24 What is the 14th term in the sequence: an = 4n + 13? -43 43 __> -69 69 What is
  7. Math *URGENT

    Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 3. Determine
  8. Algebra

    Determine whether each sequence is arithmetic or geometric. Find the next three terms. 14, 19, 24, 29, . . . A.geometric, 34, 39, 44 B.arithmetic, 32, 36, 41 C.arithmetic, 34, 39, 44 D.The sequence is neither geometric nor
  9. math

    The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric
  10. Can someone help me?!

    The 1st, 5th and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with a common ratio 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the
  11. 7th Grade Math for Steve.. or Ms. Sue

    Determine whether each sequence is arithmetic or geometric. Find the next three terms. 1. 14, 19, 24, 29, . . . (1 point) geometric, 34, 39, 44 arithmetic, 32, 36, 41 arithmetic, 34, 39, 44 ** The sequence is neither geometric nor

More Similar Questions