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Math Help - geometric sequence

  1. #1
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    geometric sequence

    find the sum of the first 12 terms of the geometric sequence 2,6,12,24
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  2. #2
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    Hello, Shorty!

    I assume there's a typo in the problem.
    . . As given, it is not a geometric sequence.


    You're expected to know these formulas for geometric sequences.

    The n^{th} term: . a_n\:=\:ar^{n-1}

    The sum of the first n terms: . S_n\:=\:a\frac{r^n - 1}{r - 1}

    . . where a is the first term and r is the common ratio.


    Find the sum of the first 12 terms of the geometric sequence: .3, 6, 12, 24 . . .

    The first term is a = 3.
    The common ratio is r = 2.

    Then: . S_{12} \;= \;3\,\frac{2^{12} - 1}{2 - 1} \:=\:3(4095) \;= \;\boxed{12,285}

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    The very least you could do is crank out the first 12 terms and add!

    . . 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072 + 6144

    What was stopping you?
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  3. #3
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    Quote Originally Posted by SHORTY View Post
    find the sum of the first 12 terms of the geometric sequence 2,6,12,24
    There's a problem with your sequence: the ratio of the terms aren't the same. For example 6/2 = 3, but 12/6 = 2. These ratios must be the same in any geometric sequence.

    -Dan
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