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What other sequences are there? Linear and quadratic sequences are particular types of sequence covered their own notes; Other sequences include geometric and Fibonacci sequences, which are looked at in more detail below; Other sequences include cube numbers (cubic sequences) and triangular numbers
- Infinite Or Finite
- In Order
- Like A Set
- As A Formula
- Many Rules
- Notation
- Arithmetic Sequences
- Geometric Sequences
- Triangular Numbers
- Fibonacci Sequence
When the sequence goes on forever it is called an infinite sequence, otherwise it is a finite sequence
When we say the terms are "in order", we are free to define what order that is! They could go forwards, backwards ... or they could alternate ... or any type of order we want!
A Sequence is like a Set, except: 1. the terms are in order(with Sets the order does not matter) 2. the same value can appear many times (only once in Sets)
Saying "starts at 3 and jumps 2 every time" is fine, but it doesn't help us calculate the: 1. 10thterm, 2. 100thterm, or 3. nth term, where ncould be any term number we want.
But mathematics is so powerful we can find more than one Rulethat works for any sequence. So it is best to say "A Rule" rather than "The Rule" (unless we know it is the right Rule).
To make it easier to use rules, we often use this special style: So a rule for {3, 5, 7, 9, ...}can be written as an equation like this: xn= 2n+1 And to calculate the 10th term we can write: x10 = 2n+1 = 2×10+1 = 21 Can you calculate x50(the 50th term) doing this? Here is another example:
In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add some value each time ... on to infinity. In Generalwe can write an arithmetic sequence like this: {a, a+d, a+2d, a+3d, ... } where: 1. ais the first term, and 2. d is the difference between the terms (called the "common difference") And...
In a Geometric Sequence each term is found by multiplying the previous term by a constant. In Generalwe can write a geometric sequence like this: {a, ar, ar2, ar3, ... } where: 1. ais the first term, and 2. r is the factor between the terms (called the "common ratio") And the rule is: xn = ar(n-1) (We use "n-1" because ar0is the 1st term)
The Triangular Number Sequenceis generated from a pattern of dots which form a triangle: By adding another row of dots and counting all the dots we can find the next number of the sequence.
The next number is found by adding the two numbers before ittogether: 1. The 2 is found by adding the two numbers before it (1+1) 2. The 21 is found by adding the two numbers before it (8+13) 3. etc... Rule is xn = xn-1 + xn-2 That rule is interesting because it depends on the values of the previous two terms. The Fibonacci Sequence is numbered fro...
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms ). The number of elements (possibly infinite) is called the length of the sequence.
Revision notes on Problem Solving with Permutations & Combinations for the CIE IGCSE Additional Maths syllabus, written by the Additional Maths experts at Save My Exams.
The number of permutations of n different items is. For 5 different items there are 5! = 5 × 4 × 3 × 2 = 120 permutations. For 6 different items there are 6! = 6 × 5 × 4 × 3 × 2 = 720 permutations. It is easy to see how quickly the number of possible permutations of different items can increase.
23 mar 2024 · MRI protocol for epilepsy is a set of MRI sequences aimed at improving sensitivity and specificity in identifying possible structural abnormalities that underlie epilepsy (e.g. mesial temporal sclerosis and malformation of cortical development ).
Two common types of mathematical sequences are arithmetic sequences and geometric sequences. An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form \(y=m x+b .\)
