Math Gcse Sequences

A rank is a set of numbers racket that ar connected in some way. For your exam, you will need to produce how to recognise different types of sequence, how to find missing terms, and how to find a general term.
Recognising sequences
A sequence is a list of numbers. The numbers are called the terms of the sequence.
There are many well-known sequences of numbers which you should be able to recognise.
Even numbers
2, 4, 6, 8, 10, 12
unmatchable numbers
1, 3, 5, 7, 9, 11
Square numbers
1, 4, 9, 16, 25, 36, 49, 64
Cube numbers
1, 8, 27, 64, 125
Powers of 2
2, 4, 8, 16, 32, 64
Powers of 10
10, 100, 1,000, 10,000, 100,000, 1,000,000
Triangle numbers
1, 3, 6, 10, 15, 21, 28

Linear sequences
1, 4, 7, 10 is a sequence starting with 1.
You scotch the next term by adding 3 to the previous term.
You are often asked to find a commandment for the nth term.

* As the common remnant is 3, try 3n.
* When n = 1, 3n = 3, and we subtract 2 to make the first term correct.
* So the nth term = 3n - 2
This method will always give for sequences where the variance between terms stays the same.

Quadratic sequences
If the difference between the terms changes, this is called a quadratic sequence.




If you use the legislation n2 + n to make a sequence, it means that:
* When n = 1 you take off 12 + 1 = 2
* When n = 2 you get 22 + 2 = 6
* When n = 3 you get 32 + 3 = 12
* When n = 4 you get 42 + 4 = 20
- giving the sequence 2, 6, 12, 20.
Here, the differences between terms are non constant, but on that point is still a pattern.
* - the first differences plus by 2 each time
* - the import increases by 2

When the second difference is constant, you have a quadratic sequence - ie, there is an n2 term.
Learn these rules:
* If the second difference is 2, you start with n2.
If the second difference is 4, you start with 2n2.
If the second difference is 6, you start with 3n2.If you want to get a full essay, order it on our website: Ordercustompaper.com



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