Nth Term My Maths Homework

Finding the nth term

Sometimes, rather than finding the next number in a linear sequence, you want to find the 41st number, or 110th number, say.

Writing out 41 or 110 numbers takes a long time, so you can use a general rule.

To find the value of any term in a sequence, use the nth term rule.

Question

What is the nth term of this sequence?

Answer

1st = 5 (5 × 1); 2nd = 10 (5 × 2); 3rd = 15 (5 × 3)

So the nth term is 5 × n or 5n

For example, to find the 10th term, work out 5 × 10 = 50. To find the 7th term, work out 5 × 7 = 35

So the 41st term is 5 × 41 = 205 and the 110th term is 5 × 110 = 550

Question

What are the nth term and the 10th term of this sequence: 2, 4, 6, ... ?

Answer

nth term = 2n

10th term = 20. To work this out, n = 10, so 2n = 2 × 10 = 20

More from Algebra

Finding the nth term of a sequence is a popular GCSE topic which usually appears on the non calculator paper of your maths exam. After reading through the example question below check out the worksheets and practice questions.


Example Question

Here is a sequence of numbers:

4, 10, 16, 22, 28

a) Write down the next two terms of the sequence.
b) Write down an expression for the nth term of this sequence.
c) Work out the 50th term of the sequence.

Solution

a) From looking at the sequence we can see that each term is 6 larger than the previous term. We say the term-to-term rule is "add 6". Therefore the next two terms are 34 and 40.

b) The nth term of a sequence is always written in the form "?n + ?".

The number in front of the "n" is always the difference to get from one term to the next. Since the difference is 6, the first part of our rule will be "6n". The rule follows the six times table: 6, 12, 18, 24... etc.

Now compare the 6 times table with our rule:

6 x table612182430
Sequence410162228

The numbers in the sequence are always 2 less than the 6 times table so we "adjust" our rule by subtracting 2. Now putting this together gives us:

nth term = 6n - 2.

c) Now we know the nth term = 6n - 2 we just need to substitute n = 50 in order to find the 50th term of the sequence.

So: The 50th term = 6 x 50 - 2
                        = 300 - 2
                  = 298

Test Yourself!

Here is a sequence of numbers:

14, 19, 24, 29, 34

a) Write down the next term of the sequence.
b) Write down an expression for the nth term of this sequence.
c) Work out the 40th term of the sequence.






Try these nth term examples courtesey of flashmaths.co.uk


Interactive worksheets on sequences:

Practice GCSE questions:

Or try this step by step guide guide to finding the nth term of a sequence.

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