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  1. #1
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    arithmethic sequences help...

    the first three terms of an arithmethic series have a sum of 24 and a product of 312. What is the fourth term of the series?
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  2. #2
    Super Member 11rdc11's Avatar
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    3,8,13,?

    You should be able to figure out the 4th term now
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  3. #3
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    how did u figure that out ?
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    The sum of an arithmetic series is given by:
    S_n = n\left(\frac{t_1+t_n}{2}\right)

    Knowing that, you can get from your given information that:
    t_1 + t_2 + t_3 = 24

    24 = 3\left(\frac{t_1+t_3}{2}\right)

    Solving both equations simultaneously yields the answer. For the second part, simply find the common difference and add it to the third term.
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    Quote Originally Posted by gendut3 View Post
    the first three terms of an arithmethic series have a sum of 24 and a product of 312. What is the fourth term of the series?
    a + (a + d) + (a + 2d) = 24 => 3a + 3d = 24 => a + d = 8 => a = 8 - d .... (1)

    a(a + d)(a + 2d) = 312 .... (2)

    Substitute (1) into (2): (8 - d)(8)(8 + d) = 312 => (8 - d)(8 + d) = 39 => 64 - d^2 = 39 => d^2 = 25 => d = 5 or -5.

    Case 1: d = 5 => a = 3.

    Case 2: d = -5 => a = 13.

    It's left for you to find the fourth term of the series in each case.
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