Arithmetic Sequences (the nth term)
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  • Introduction
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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 x 5 - 2 = 30 - 2 = 28

  • Question 1
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Work out the nth term in this sequence:

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

  • Question 2
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Work out the nth term in this sequence:

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

  • Question 3
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Work out the nth term in this sequence:

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

  • Question 4
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Work out the nth term in this sequence:

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

  • Question 5
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Work out the nth term in this sequence:

1, 3, 5, 7, 9, 11  ...

  • Question 6
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Work out the nth term in this sequence:

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

  • Question 7
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Work out the nth term in this sequence:

 4, 7, 10, 13, 16, 19 ...

  • Question 8
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Work out the nth term in this sequence:

 1, 6, 11, 16, 21, 26 ...

  • Question 9
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Work out the nth term in this sequence:

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

  • Question 10
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Work out the nth term in this sequence:

9, 13, 17, 21, 25, 29 ... 

Progress