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

Oct 18, 2016

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

#### Explanation:

${a}_{n + 1} = {a}_{n} - 3$ and ${a}_{1} = 12$

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 ${a}_{1} = 12$.

The 2nd term is ${a}_{2} = {a}_{1 + 1} = {a}_{1} - 3 = 12 - 3 = 9$

The 3rd term is ${a}_{3} = {a}_{2 + 1} = {a}_{2} - 3 = 9 - 3 = 6$

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

So, ${a}_{4} = 3$ and ${a}_{5} = 0$.

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