FINDING THE Nth TERM - RGS Info
Finding the nth Term
This is also known as finding a formula for the sequence of numbers.
Consider the sequence of numbers
1 4 9 16 25 36…
Hopefully we recognise these as the square numbers
12 22 32 42 52 62….
So we could say that the general term was n2
We write
Un = n2
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Un is used as shorthand for “the nth term”
Some sequences are not so easy to spot though!
Consider the sequence
4 7 10 13 16…..
In this sequence there is a common difference between the terms of 3 so the formula must contain 3n.
The term before the sequence starts in this case is 1
So the formula becomes
Un = 3n + 1
Similarly the sequence
3 8 13 18 23 28…..
would become
Un = 5n – 2
And if the sequence decreases
21 17 13 9 5….
would become
Un = -4n + 25
or better written as
Un = 25 - 4n
If you have an nth term formula, you can use it to find the value of any term quickly:
Example 1
An arithmetic sequence starts 30 34 38 42 …, what is the 100th term?
30 34 38 42 … has a common difference of 4
The previous term would be 26
So, Un = 4n +26
So, U100 = 4 × 100 +26 = 426
This is much quicker than listing the whole sequence!
Example 2
An arithmetic sequence starts 48 41 34 27 …, what is the 100th term?
48 41 34 27 … has a common difference of -7
The previous term would be 55
So, Un = -7n + 55 = 55 – 7n
So, U100 = 55 – 7 × 100 = -645
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