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Math Help - sequence general formula

  1. #1
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    sequence general formula

    Find a formula for sn, n 1. 4, 12, 28, 60, 124, ...

    im having a really hard time with figuring how to find the general terms... can anyone give me some hints or other ways to look for the general terms?
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  2. #2
    Super Member girdav's Avatar
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    I think s_n = 2s_{n-1}+4.
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  3. #3
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    Quote Originally Posted by acosta0809 View Post
    Find a formula for sn, n 1. 4, 12, 28, 60, 124, ...
    Try stuff, and see if you can discern any patterns.

    What do you multiply 4 by to get 12? What do you multiply 12 by to get 28? Does this lead to any apparent patterns?

    What do you add by to go from 4 to 12? What do you add by to go from 12 to 28? Does this lead to any apparent patterns?

    Can you relates primes or powers to the numbers? And so forth.

    Hint: 4 - 0 = 4 = 2^2
    12 - 4 = 8 = 2^3
    28 - 12 = 16 = 2^4
    60 - 28 = 32 = 2^5

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  4. #4
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    Quote Originally Posted by acosta0809 View Post
    Find a formula for sn, n 1. 4, 12, 28, 60, 124, ...

    im having a really hard time with figuring how to find the general terms... can anyone give me some hints or other ways to look for the general terms?
    2^2 \times (2-1) = 2^2 \times (2^1-1)
    2^2 \times (4-1) = 2^2 \times (2^2-1)
    2^2 \times (8-1) = 2^2 \times (2^3-1)
    2^2 \times (16-1) = 2^2 \times (2^4-1)
     2^2 \times (32-1) = 2^2 \times (2^5-1)
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  5. #5
    MHF Contributor Calculus26's Avatar
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    a1 = 4= 2^3 -4

    a2 = 12 = 2^4 - 4

    a3 = 28 = 2^5 -4

    an = 2^(n+2) - 4 = 4(2^(n) - 1)
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