Need help with this problem. It states: Determine the number of n-digit quaternary (0, 1, 2, 3) sequences (in closed form) where there is never a 3 anywhere to the right of a 0. My current solution: I split it up into two parts, one for if there is a 0 in the sequence and one without. I've gathered that there are 3^(n-1) possibilities if the first digit is a 0 and you add it with the remaining which is 3^n? But something seems missing. Please help!!! Also how should I set up my characteristic polynomial? (S(k))? I have S(k) = S(k-1) + k*3S(k-1) and trying to solve for the coefficients. But it doesn't seem to be quite right. Please help and thank you!

Need help with this problem. It states: Determine the number of n-digit quaternary (0, 1, 2, 3) sequences (in closed form) where there is never a 3 anywhere to the right of a 0. My current solution: I split it up into two parts, one for if there is a 0 in the sequence and one without. I've gathered that there are 3^(n-1) possibilities if the first digit is a 0 and you add it with the remaining which is 3^n? But something seems missing. Please help!!! Also how should I set up my characteristic polynomial? (S(k))? I have S(k) = S(k-1) + k*3S(k-1) and trying to solve for the coefficients. But it doesn't seem to be quite right. Please help and thank you!

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter12: Sequences, Series And Binomial Theorem

Section: Chapter Questions

Problem 327PT: Find the twenty-third term of an arithmetic sequence whose seventh term is 11 and common difference...

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