Show that the sequence a_{n} is an solution of the recurrence relation PS

pancha3

pancha3

Answered question

2021-09-18

Show that the sequence an is an solution of the recurrence relation an=3an1+4an2 if an=0.

Answer & Explanation

diskusje5

diskusje5

Skilled2021-09-19Added 82 answers

Given:
an=0
n=0,1,2,...
To prove: an=3an1+4an2,n2.
Proof
Replace n in an=0 by n-1:
an1=0
Replace n in an=0 by n-2:
an2=0
We will start from the expression 3an1+4an2 and prove that this term has to be equal to an(when n2).
Let us use the two previous expressions derived for an1 and an2
3an1+4an2=3(0)+4(0)=0+0=0=an

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