Lesson 1 Flashcards
What is sequence?
an ordered list of objects or numbers that follow a pattern.
What are the types of sequence?
Arithmetic and geometric sequence.and more.
How many types are in the sequence?
4.
What is Arithmetic sequences?
An arithmetic sequence is an ordered set of numbers that have a common difference between each term.
Ex:
If we add or subtract by the same number each time to make the sequence, it is an arithmetic sequence
What is Geometric sequences?
A geometric sequence is an ordered set of numbers that progresses by multiplying or dividing each term by a common ratio.
If we multiply or divide by the same number each time to make the sequence, it is a geometric sequence
What is Quadratic sequences?
A quadratic sequence is an ordered set of numbers that follow a rule based on the sequence n2 = 1, 4, 9, 16, 25, … (the square numbers).
The difference between each term is not equal, but the second difference is
Explain the Special sequences?.
You will need to be able to recognise some important special sequences.
What are the Special sequences?.
square numbers, cube numbers,triangular numbers,and Fibonacci numbers.
What is square numbers?
A square number is the result when a number is multiplied by itself.
What is the cube numbers?
A cube number is the result when a number is multiplied by itself three times.
What is the triangular numbers?
The triangular numbers as numbers that can form a triangular dot pattern. They are also special type of quadratic sequence.
What is the Fibonacci numbers?
The Fibonacci Sequence of numbers by adding the previous two numbers together to work out the next term.
How will you find the sequence rule to find a term?.
We use the nth term of a sequence to work out a particular term in a sequence.
By substituting in the number of the term we want to find as ‘n’ we can generate the specific term in the sequence.
E.g.
What is the nth term and the 21st term of this sequence?
4, 10, 16, 22, …
The nth term of this sequence is 6n – 2.
To find the 21st term, n = 21
(6 x 21) – 2 = 124
The 21st term is 124.
How will you find the nth term of a sequence?
The nth term is a formula that enables us to find any term in a sequence.
We will need to be able to find the nth term of a linear (arithmetic) sequence, and the nth term of a quadratic sequence.
We can make a sequence using the nth term by substituting different values for the term number n into it.
Wgat are the steps to find the 1nth term of a linear sequence?
Step 1: find the common difference for the sequence.
Step 2: multiply the values for n = 1, 2, 3, … by the common difference.
Step 3: add or subtract a number to obtain the sequence given in the question.
What are the steo to find the 2nth term of a quadratic sequence?
Step 1: find the first difference (d1) and second difference (d2) for the sequence.
Step 2: Halve the second difference to find a, the coefficient of n2.
(
d
2
2
=
a
)
Step 3: Subtract an2 from the original sequence.
Step 4: If this produces a linear sequence, find the nth term of it.
Step 5: Add the nth term for the linear sequence to an2 to work out the nth term of the quadratic sequence.
