# Nth Term Maths Help For Homework

## Finding the nth term

Sometimes, rather than finding the next number in a linear sequence, you want to find the 41^{st} number, or 110^{th} 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 n^{th} term rule.

- Question
What is the n

^{th}term of this sequence?

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

So the n

^{th}term is 5 × n or 5n

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

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

- Question
What are the n

^{th}term and the 10^{th}term of this sequence: 2, 4, 6, ... ?

- Answer
n

^{th}term = 2n10

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

More from Algebra

^{th}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 n

^{th}term of this sequence.

c) Work out the 50

^{th}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 n

^{th}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 table | 6 | 12 | 18 | 24 | 30 |

Sequence | 4 | 10 | 16 | 22 | 28 |

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:

### n^{th} term = 6n - 2.

c) Now we know the n^{th}term = 6n - 2 we just need to substitute n = 50 in order to find the 50

^{th}term of the sequence.

So: The 50

^{th}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 n^{th} term of this sequence.

c) Work out the 40^{th} term of the sequence.