# What are the first 5 terms of the sequence?

Apr 15, 2018

$0 , 1 , 1 , 0 , - 1$

#### Explanation:

We're given the fact that ${a}_{n} = {a}_{n - 1} - {a}_{n - 2}$

A verbal interpretation tells us that if we know the first two terms of the sequence, we can use them to find the next term. From there, we can use the previous two terms to always find the next term.

So, knowing that ${a}_{1} = 0 , {a}_{2} = 1 ,$ then

${a}_{3} = {a}_{3 - 1} - {a}_{3 - 2} = {a}_{2} - {a}_{1}$

${a}_{3} = 1 - 0 = 1$

${a}_{4} = {a}_{3} - {a}_{2} = 1 - 1 = 0$

${a}_{5} = {a}_{4} - {a}_{3} = 0 - 1 = - 1$

So, since we already know the first two terms, we've found the first five terms:

$0 , 1 , 1 , 0 , - 1$