Step by step
The question
Question: 2, 5, 8, 11, …: find term 20.
A sequence is a list of numbers in order.
1 Find the difference
We add 3 every time.
A list like this is an arithmetic sequence.
The number we add is called the difference: d = 3.
2 Find the rule
Term 1 is 2.
a₁ is term 1, a₂ is term 2.
So aₙ is term number n.
Term 2: we add 3 one time.
Term 3: we add it two times.
We add 3 one time less than the term number.
So for term n, we add 3, (n − 1) times.
This rule works for every arithmetic sequence: the first term, plus (n − 1) times the difference.
3 Find term 20
For term 20, n is 20.
We put 20 in place of n.
Brackets come first.
20 minus 1 is 19.
Times comes before plus.
19 times 3 is 57.
2 plus 57 is 59.
So term 20 is 59.
4 Check
Let's check the rule with a term we know.
Put n = 4.
We get 11.
That is term 4 in the list.
So the rule is right!
Let's look back.
First: find the difference.
Then: find the rule.
Then: find term 20.
Last: check.