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Math Help - Missing terms in arithmetic & geometric sequences.

  1. #1
    Junior Member
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    Question Missing terms in arithmetic & geometric sequences.

    Hello, I have no idea how to go about when finding, "missing terms." I would like to know how to at least start solving these type of problems. Many thanks in advance!

    A. "Fill in the missing terms for each arithmetic sequence:"
    1) 3, __,__,__,__,__,__,__,__,__, 75

    2) __,__,__, -4, __,__,__,__,26


    B. "Fill in the missing terms for each geometric sequence:"
    1) 100,__,4

    2) 2,__,__,__,162
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  2. #2
    Super Member

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    Hello, Mulya66!

    A. Fill in the missing terms for each arithmetic sequence.

    You're expected to know the formula for the nth term of an arithmetic sequence:
    . . . . a
    n .= .a1 + (n-1)d
    where a
    1 is the first term and d is the common difference.

    1) .3, __, __, __, __, __, __, __, __, __, 75
    We see that: .a1 = 3 .and .a11 = 75

    Since .a
    11 .= .a1 + 10d
    . . we have: .3 + 10d .= .75 . . . . d = 7.2

    The sequence is: .3, 10.2, 17.4, 24.6, 31.8, 39, 46.2, 53.4, 60.6, 67.8, 75



    2) .__, __, __, -4, __, __, __, __, 26
    We are given: .a4 = -4 .and .a9 = 26

    So we have: .a
    1 + 3d .= .-4 . [1]
    . - . . o . . . . a
    1 + 8d .= .26 ([2]

    Subtract [1] from [2]: .5d = 30 . . . . d = 6

    Substitute into [1]: .a
    1 + 36 .= .-4 . . . . a1 = -22

    The sequence is: .-22, -16, -10, -4, 2, 8, 14, 20, 26



    B. "Fill in the missing terms for each geometric sequence.
    You're expected to know the formula for the nth term of a geometric sequence.
    . . . . a
    n .= .a1r^{n-1}
    where a
    1 is the first term and r is the common ratio.

    1) . 100, __, 4
    We are given: .a1 = 100 .and .a3 = 4

    Then: .a
    3 .= .100r .= .4 . . . . r = 1/5

    The sequence is: .100, 20, 4



    2) .2, __, __, __, 162

    I'll let you work on this one . . .

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  3. #3
    Junior Member
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    Thank you.

    Thank you so much.

    Quote Originally Posted by Soroban View Post
    Hello, Mulya66!

    2, __,__,__,162

    I'll let you work on this one . . .

    Following your steps, I found that r = 3. Thus, the missing numbers are 6, 18, and 54. I'm proud of myself, thanks again. :-)
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