Find the Rule of Linear Number Sequences

In this activity, we will work out rules to help us find any term in a given sequence.

We call this the nth term.

n stands for 'any' term in the sequence. 

Let's have a look at one .....

3, 5, 7, 9, .....

We can see that the sequence is going up in 2s

That is the two times table or multiply the term by 2

We call this 2n

However, the 2 times table is 2, 4, 6, 8, ....

The first term of our sequence is 3

so, we need to add 1

The rule becomes 2n + 1

Now, we can find any term in that sequence by substituting for n!

Let's find the 10th term.

Remember that 'n' stands for the number of the term, so for the 10th term, n = 10

2n + 1 = 2 x 10 + 1

10th term = 21

Let's try a question!

Example

a)  Find the nth term rule of the linear sequence:

5, 8, 11, 14, 17, ......

b)  Find the 15th term in the sequence.

Answer

a)  We can see that the sequence is going up in 3s

This is the 3 times table. We call this 3n

The 3 times table is 3, 6, 9, .....

The first term of our sequence is 5

Therefore, we need to add 2

The nth term rule is 3n + 2

b) We can use this rule to find the 15th term

n = 15

3n + 2 = 3 x 15 + 2

= 47

The 15th term = 47

Let's try some!