a_1 = 3, a_n = a_(n-1) + 4, find the first 5 terms

Step by step

The question

Question: a₁ = 3 and aₙ = aₙ₋₁ + 4.

Find the first 5 terms.

aₙ₋₁ means the term just before aₙ.

A rule that makes each term from the term before is called recursive.

Careful!

aₙ₋₁ is the term before, not the number n − 1.

For term 2 we put in a₁, which is 3.

1 Start with a₁

The start is given: a₁ = 3.

2 Use the rule again and again

Term 2: n = 2, so the term before is a₁.

We put in 3.

3 + 4 is 7.

Term 3: the term before is a₂, which is 7.

7 + 4 is 11.

Term 4: 11 + 4 is 15.

Term 5: 15 + 4 is 19.

3 Write the list

So the first 5 terms are 3, 7, 11, 15, 19.

4 Check

Let's check by going back.

The rule did plus 4.

Going back, we do the opposite: take away 4.

From 19: 19 − 4 is 15, term 4.

We land on 3, the start.

It works!

Let's look back.

First: start with a₁.

Then: use the rule again and again.

Then: write the list.

Last: check.