 # Arithmetic Sequences (the nth Term)

In this worksheet, students find the nth term in arithmetic sequences. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Sequences to Find the nth Term

Difficulty level:   ### QUESTION 1 of 10

In an arithmetic sequence like this:

4, 10, 16, 22, 28, 34 ...

the nth term is found as follows:

Step 1

Find the common difference between the terms.

Here it is 6.

Step 2

The common difference is the coefficient of n.

Here we get 6n.

Step 3

Compare this to the actual sequence and adjust the formula by adding or subtracting a fixed number.

Here 6n would give us the terms 6, 12, 18, 24, 30 etc. ... which is 2 more than our sequence of 4, 10, 16, 22, 28 etc.

So we must subtract 2.

So the nth term is 6n - 2.

We can test this by putting in n = 5 to check that the 5th term is really 28.

It is because 6 × 5 - 2 = 30 - 2 = 28.

Work out the nth term in this sequence:

4, 5, 6, 7, 8, 9 ...

Work out the nth term in this sequence:

3, 5, 7, 9, 11, 13  ...

Work out the nth term in this sequence:

4, 7, 10, 13, 16 ...

Work out the nth term in this sequence:

7, 10, 13, 16, 19 ...

Work out the nth term in this sequence:

11, 16, 21, 26, 31 ...

Work out the nth term in this sequence:

17, 24, 31, 38, 45 ...

Work out the nth term in this sequence:

17, 21, 25, 29, 33 ...

Work out the nth term in this sequence:

21, 25, 29, 33, 37 ...

Work out the nth term in this sequence:

-2, 2, 6, 10, 14 ...

Work out the nth term in this sequence:

-2, 5, 12, 19, 26 ...

• Question 1

Work out the nth term in this sequence:

4, 5, 6, 7, 8, 9 ...

n+3
n + 3
EDDIE SAYS
Common difference is 1.
• Question 2

Work out the nth term in this sequence:

3, 5, 7, 9, 11, 13  ...

2n+1
2n + 1
EDDIE SAYS
Common difference is 2.
• Question 3

Work out the nth term in this sequence:

4, 7, 10, 13, 16 ...

3n+1
3n + 1
EDDIE SAYS
Common difference is 3.
• Question 4

Work out the nth term in this sequence:

7, 10, 13, 16, 19 ...

3n+4
3n + 4
EDDIE SAYS
Common difference is 3.
• Question 5

Work out the nth term in this sequence:

11, 16, 21, 26, 31 ...

5n+6
5n + 6
EDDIE SAYS
Common difference is 5.
• Question 6

Work out the nth term in this sequence:

17, 24, 31, 38, 45 ...

7n+10
7n + 10
EDDIE SAYS
Common difference is 7.
• Question 7

Work out the nth term in this sequence:

17, 21, 25, 29, 33 ...

4n+13
4n + 13
EDDIE SAYS
Common difference is 4.
• Question 8

Work out the nth term in this sequence:

21, 25, 29, 33, 37 ...

4n+17
4n + 17
EDDIE SAYS
Common difference is 4.
• Question 9

Work out the nth term in this sequence:

-2, 2, 6, 10, 14 ...

4n-6
4n - 6
EDDIE SAYS
Common difference is 4.
• Question 10

Work out the nth term in this sequence:

-2, 5, 12, 19, 26 ...

7n-9
7n - 9
EDDIE SAYS
Common difference is 7. 