Step by step
The question
Question: 5, 9, 13, 17, …: find term 30.
A sequence is a list of numbers in order.
1 Find the difference
From 5 to 9, we add 4.
From 9 to 13, we add 4 again.
We add 4 every time.
A list like this is an arithmetic sequence.
The number we add is called the difference: d = 4.
2 Find the rule
Term 1 is 5.
a₁ is term 1, a₂ is term 2.
So aₙ is term number n.
Term 2: we add 4 one time.
Term 3: we add it two times.
We add 4 one time less than the term number.
So for term n, we add 4, (n − 1) times.
This rule works for every arithmetic sequence: the first term, plus (n − 1) times the difference.
3 Find term 30
For term 30, n is 30.
We put 30 in place of n.
Everyone uses the same order, so we all get the same answer.
Brackets come first.
30 minus 1 is 29.
Times comes before plus.
29 times 4 is 116.
We write them in a column: ones under ones, tens under tens.
We add each column, from the right.
5 + 6 = 11.
We write 1 and carry the 1 to the next column.
1 + 1 = 2.
Only 1 in this column, so it comes down: 1.
5 plus 116 is 121.
So term 30 is 121.
4 Check
Let's check the rule with a term we know.
Put n = 4.
We get 17.
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 30.
Last: check.