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Arithmetic Sequences (the Nth Term)

In this worksheet, students find the Nth term in simple linear sequences.

'Arithmetic Sequences (the Nth Term)' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Sequences to Find the nth Term

Difficulty level:  

Worksheet Overview

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 (this just means the number in front.) 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 x 5 - 2 = 30 - 2 = 28

 

For this worksheet, It is important that you do not put spaces in your answer (For example, you would need to put in 5n-3 instead of 5n  -  3. If you put in spaces, the system will mark it as wrong.

Work out the nth term in this sequence:

1, 2, 3, 4, 5, 6 ...

Work out the nth term in this sequence:

2, 4, 6, 8, 10, 12 ...

Work out the nth term in this sequence:

5, 10, 15, 20, 25, 30 ...

Work out the nth term in this sequence:

2, 3, 4, 5, 6, 7 ...

Work out the nth term in this sequence:

1, 3, 5, 7, 9, 11  ...

Work out the nth term in this sequence:

1, 4, 7, 10, 13, 16 ...

Work out the nth term in this sequence:

 4, 7, 10, 13, 16, 19 ...

Work out the nth term in this sequence:

 1, 6, 11, 16, 21, 26 ...

Work out the nth term in this sequence:

10, 17, 24, 31, 38, 45 ...

Work out the nth term in this sequence:

9, 13, 17, 21, 25, 29 ... 

  • Question 1

Work out the nth term in this sequence:

1, 2, 3, 4, 5, 6 ...

CORRECT ANSWER
n
EDDIE SAYS
Common difference is 1.
No need to adjust.
  • Question 2

Work out the nth term in this sequence:

2, 4, 6, 8, 10, 12 ...

CORRECT ANSWER
2n
EDDIE SAYS
Common difference is 2.
No need to adjust.
  • Question 3

Work out the nth term in this sequence:

5, 10, 15, 20, 25, 30 ...

CORRECT ANSWER
5n
EDDIE SAYS
Common difference is 5.
No need to adjust.
  • Question 4

Work out the nth term in this sequence:

2, 3, 4, 5, 6, 7 ...

CORRECT ANSWER
n+1
EDDIE SAYS
Common difference is 1.
Add 1 to adjust.
  • Question 5

Work out the nth term in this sequence:

1, 3, 5, 7, 9, 11  ...

CORRECT ANSWER
2n-1
EDDIE SAYS
Common difference is 2.
Subtract 1 to adjust.
  • Question 6

Work out the nth term in this sequence:

1, 4, 7, 10, 13, 16 ...

CORRECT ANSWER
3n-2
EDDIE SAYS
Common difference is 3.
Subtract 2 to adjust.
  • Question 7

Work out the nth term in this sequence:

 4, 7, 10, 13, 16, 19 ...

CORRECT ANSWER
3n+1
EDDIE SAYS
Common difference is 3.
Add 1 to adjust.
  • Question 8

Work out the nth term in this sequence:

 1, 6, 11, 16, 21, 26 ...

CORRECT ANSWER
5n-4
EDDIE SAYS
Common difference is 5.
Subtract 4 to adjust.
  • Question 9

Work out the nth term in this sequence:

10, 17, 24, 31, 38, 45 ...

CORRECT ANSWER
7n+3
EDDIE SAYS
Common difference is 7.
Add 3 to adjust.
  • Question 10

Work out the nth term in this sequence:

9, 13, 17, 21, 25, 29 ... 

CORRECT ANSWER
4n+5
EDDIE SAYS
Common difference is 4.
Add 5 to adjust.
---- OR ----

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