KS3 Grade 6 - SEQUENCES
Lesson 3...FINDING THE Nth TERM OF A SEQUENCE
![Picture](/uploads/1/3/3/4/13343229/5997228.jpg)
To find the nth term of any given arithmetic sequence use the following method
(1) Find the difference between the value of each term (term-to-term rule)
(2) Multiply this value by the unknown n
(3) Substitute the value 1 for n and compare the result with the value of the first term in the sequence
(4) Identify what value must be added or subtracted to produce the first term of the sequence
(5) Check that this rule is correct for other terms in the sequence
Eg. Find the nth term for the following sequence 3, 7, 11, 15, 19, ...
(1) The difference is +4.
(2) Multiply +4 by n to get 4n
(3) Substituting in the value 1 leaves the answer 4
(4) This is 1 number larger than the associated term in the sequence so I must subtract 1
(5) This produces the nth term T(n) = 4n - 1
TASK 1 - Textbook Pg229 Ex6
HOMEWORK - Sequences worksheet, AQA Foundation paper
(1) Find the difference between the value of each term (term-to-term rule)
(2) Multiply this value by the unknown n
(3) Substitute the value 1 for n and compare the result with the value of the first term in the sequence
(4) Identify what value must be added or subtracted to produce the first term of the sequence
(5) Check that this rule is correct for other terms in the sequence
Eg. Find the nth term for the following sequence 3, 7, 11, 15, 19, ...
(1) The difference is +4.
(2) Multiply +4 by n to get 4n
(3) Substituting in the value 1 leaves the answer 4
(4) This is 1 number larger than the associated term in the sequence so I must subtract 1
(5) This produces the nth term T(n) = 4n - 1
TASK 1 - Textbook Pg229 Ex6
HOMEWORK - Sequences worksheet, AQA Foundation paper
Lesson 2...GENERATING SEQUENCES (POSITION-TO-TERM)
![Picture](/uploads/1/3/3/4/13343229/8773094.jpg?165)
To find the value of a particular term in a sequence dependant on its position in the sequence, we use a POSITION-TO-TERM rule. For any particular sequence this rule is also known as the nth term for that sequence as is written as an expression using an unknown value 'n'
Eg. Generate the first three terms of a sequence using the nth term T(n) = 11n - 5
This is done by substituting the values 1, 2, 3 into the expression as below
T(1) = (11 x 1) - 5 = 6
T(2) = (11 x 2) - 5 = 17
T(3) = (11 x 3) - 5 = 28
Therefore the sequence is 6, 17, 28, ...
The nth term can also be quickly used to find any term within that sequence, again using substitution
Eg. Find the 24th term in the sequence in the previous example
T(24) = (11 x 24) - 5 = 259
TASK 1 - Textbook Pg221 Ex4
HOMEWORK - None set
Eg. Generate the first three terms of a sequence using the nth term T(n) = 11n - 5
This is done by substituting the values 1, 2, 3 into the expression as below
T(1) = (11 x 1) - 5 = 6
T(2) = (11 x 2) - 5 = 17
T(3) = (11 x 3) - 5 = 28
Therefore the sequence is 6, 17, 28, ...
The nth term can also be quickly used to find any term within that sequence, again using substitution
Eg. Find the 24th term in the sequence in the previous example
T(24) = (11 x 24) - 5 = 259
TASK 1 - Textbook Pg221 Ex4
HOMEWORK - None set
Lesson 1...GENERATING SEQUENCES (TERM-TO-TERM)
![Picture](/uploads/1/3/3/4/13343229/7859321.jpg?322)
A NUMBER SEQUENCE is a set of numbers in a given order which follow a pattern
Each value in a number sequence is called a TERM
FINITE sequences have a limited number of terms
An INFINITE sequence has an unlimited number of terms and continues forever
The terms in a sequence may increase, or decrease, in value and can be described using words as follows
Eg. Start at 0.3 and count on in steps of 0.6
0.3, 0.9, 1.5, 2.1, 2.7, ...
The rule for getting from one term to the next term is known as the TERM-TO-TERM rule
TASK 1 - Textbook Pg218 Ex3
HOMEWORK - None set
Each value in a number sequence is called a TERM
FINITE sequences have a limited number of terms
An INFINITE sequence has an unlimited number of terms and continues forever
The terms in a sequence may increase, or decrease, in value and can be described using words as follows
Eg. Start at 0.3 and count on in steps of 0.6
0.3, 0.9, 1.5, 2.1, 2.7, ...
The rule for getting from one term to the next term is known as the TERM-TO-TERM rule
TASK 1 - Textbook Pg218 Ex3
HOMEWORK - None set