recursive formula

**mathh18** · March 1st 2010, 07:06 PM

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!!

**Soroban** · March 1st 2010, 09:16 PM

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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