How would you proceed to find the generating function of the following sequence? $$a_n = 5\times 7^n - 3\times 4^n$$ I have no idea where to start for cases where the index appears as exponent.
Thanks in advance!
2026-04-13 08:57:12.1776070632
Generating function for sequence $a_n = 5\times 7^n - 3\times 4^n$
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Hint: The sequence satisfies the recurrence $a_{n+2}=11a_{n+1}-28a_n$.
This comes from expanding $(x-7)(x-4)$.