Step by step
The question
Question: 7, 13, 19, 25, …: find term 25.
A sequence is a list of numbers in order.
1 Find the difference
From 7 to 13, we add 6.
From 13 to 19, we add 6 again.
We add 6 every time.
A list like this is an arithmetic sequence.
The number we add is called the difference: d = 6.
2 Find the rule
Term 1 is 7.
a₁ is term 1, a₂ is term 2.
So aₙ is term number n.
Term 2: we add 6 one time.
Term 3: we add it two times.
We add 6 one time less than the term number.
So for term n, we add 6, (n − 1) times.
This rule works for every arithmetic sequence: the first term, plus (n − 1) times the difference.
3 Find term 25
For term 25, n is 25.
We put 25 in place of n.
Everyone uses the same order, so we all get the same answer.
Brackets come first.
25 minus 1 is 24.
Times comes before plus.
24 times 6 is 144.
We write them in a column: ones under ones, tens under tens.
We add each column, from the right.
7 + 4 = 11.
We write 1 and carry the 1 to the next column.
1 + 4 = 5.
Only 1 in this column, so it comes down: 1.
7 plus 144 is 151.
So term 25 is 151.
4 Check
Let's check the rule with a term we know.
Put n = 4.
We get 25.
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 25.
Last: check.