a_1 = 5, a_n = a_(n-1) + 4, write the explicit rule

Step by step

The question

Question: a₁ = 5 and aₙ = aₙ₋₁ + 4.

Write the explicit rule: aₙ with n in it.

aₙ₋₁ means the term just before aₙ.

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

1 Read the rule

The first terms: 5, 9, 13.

We add the same number every time.

So it is arithmetic, with d = 4.

2 Write the explicit rule

The rule from the sequences lesson: the first term, plus (n − 1) times the difference.

Careful!

Not 4n plus the start.

Term 1 adds no jumps yet, so we add d only n − 1 times.

Put in a₁ = 5 and d = 4.

The bracket is times 4.

n times 4 is 4n.

−1 times 4 is −4.

Plain numbers go together: 5 − 4 is 1.

So aₙ = 4n + 1.

3 Check

Let's check with term 3.

The recursive rule gave 13.

The explicit rule with n = 3 gives 13 too.

It works!

Let's look back.

First: read the rule.

Then: write the explicit rule.

Last: check.