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You finally get an allowance . You put $2 away in January, 4$ away in February, $8 away in March, $16 away in April and followed this saving pattern through to December. How much money do you have in 12 months? Please explain

  • math -

    2+4+8+...+2^n = 2^(n+1)-2

  • math -

    2,4,8,16,......
    This is a geometric sequence. That means the same number is multiplied, which is 2.
    You could calculate this way;
    {a, ar, ar^2, ar^3, ar^4, …..}

    2, 2x2 2x2^2 2x2^3 2x2^4

    (2, 4, 8, 16, 32, ...)
    a = the 1st term.
    common ratio = 2 > the factor between terms.
    Formula:
    an = ar^(n - 1)
    an = 2 x 2^(n – 1)
    a = 2 > 1st term
    r = 2 > common ratio
    n = nth term > the term you're going to.
    The third and fourth term you already know.
    a(3)= 2 x 2^(3 - 1)
    a(3)= 2 x 2^2
    a(3)= 2 x 4
    a(3) = $8

    a(4)= 2 x 2^(4 - 1)
    a(4)= 2 x 2^3
    a(4)= 2 x 8
    a(4)= $16

    a(12)= 2 x 2^(12 - 1)
    a(12)= 2 x 2^11
    a(12)= 2 x 2048
    a(12)= %4096
    Answer:
    $4096

  • math -

    Chelle's solution gives the 12th term, but does not show the sum of all 12 terms, which was what was asked.

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