nth term of a sequence - 6th Oct 2008
In the first lesson on sequences we have been looking at how to find the nth term of a sequence and use it to find any term.
Definitions
Here are some definitions of words you need to know.
Term - a number or variable (letter) or the product of a number and variable(s). e.g. 3, x, 3x
nth term - this phrase is used to describe a ‘general’ term in a sequence. You can use the nth term to find the terms of a sequence. The nth term might look something like 2n + 4, n - 2 or n² + 6
Term-to-term rule - the rule that describes the difference between terms in a sequence. e.g. +3 or -5
Linear sequence - a sequence where the differences between the terms are all the same.
Using the nth term to find a sequence
we can find the terms of a sequence if we know the nth term.
Given the nth term 2n + 3
We find the first term by replacing n with 1 in the formula. So the first term is
2 x 1 + 3 = 5
In the same way we can find the second term by replacing n with 2 in the formula
2 x 2 + 3 = 7
We can do this for every term. For example the 100th term would be
2 X 100 + 3 = 203
So the first five terms in this sequence whose nth term is 2n + 3 are
5, 7, 9, 11, 13, …
The term to term rule for this sequence is + 2, because you add 2 to each term to find the next.
Finding the nth term
To find the formula for the nth term of a sequence you use the formula as below.
[...] We then continued to work on finding the formula for the nth term of sequences. This is detailed in the post from last lesson. [...]