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Math Help - recursive formula

  1. #1
    Junior Member
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    recursive formula

    the next series is 0, 30, 240, 1020, 3120..what is the recursive formula?

    the next series is 7, 63, 511, 4096..what is the recursive formula?

    help on any of these would be great! thank you!!
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  2. #2
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    Hello, mathh18!

    Is there a typo in the second series?


    7,\:63,\:511,\:4096,\:\hdots
    . . . . . . . .?

    I hope that it's supposed to be: . 7,\:63,\:511,\:409{\color{red}5},\:\hdots

    . . because I recognize these: . 2^3-1,\;\;2^6-1,\;\;2^9-1,\;\;2^{12}-1,\;\;\hdots


    Given a term of the sequence, to get the next term:

    . . add 1, multiply by 8, subtract 1.


    That is: . a_{n+1} \;=\;8(a_n + 1) - 1

    . . which simplifies to: . a_{n+1} \;=\;8a_n + 7

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