How do you find the first five terms of each sequence a_1=12a1=12, a_(n+1)=a_n-3an+1=an3?

1 Answer
Oct 18, 2016

The first 5 terms are 12, 9, 6, 3, 012,9,6,3,0

Explanation:

a_(n+1)=a_n-3an+1=an3 and a_1=12a1=12

Find the first five terms.

This is a recursively defined sequence, which means you use the previous term to find the next.

The first term is a_1=12a1=12.

The 2nd term is a_2=a_(1+1)=a_1-3=12-3=9a2=a1+1=a13=123=9

The 3rd term is a_3=a_(2+1)=a_2-3=9-3=6a3=a2+1=a23=93=6

Note that you are subtracting 3 to find the next term.

So, a_4=3a4=3 and a_5=0a5=0.

The first 5 terms are 12, 9, 6, 3, 012,9,6,3,0.