21.1Introduction
• continue a given number sequence
• recognise patterns in sequences and relationships between different
sequences
• generalise sequences as simple algebraic statements
Includes linear sequences, quadratic and cubic sequences, exponential
sequences and simple combinations of these.
Including expressions for the nth term.
21.2-Linear Sequences
Generate terms of a sequence from either a term-to-term or a position-to- term rule
Recognise and use sequences of triangular, square and cube numbers,
simple arithmetic progressions, Fibonacci type sequences, quadratic
sequences, and simple geometric progressions (rn where n is an integer,
and r is a rational number > 0)
deduce expressions to calculate the nth term of linear sequences
Question 1 : Calculate the next 3 terms of the following sequence :
1 , 4, 7, 10, 13……..
Question 2 : The nth term of a sequence is 12n – 5 , Calculate the first 5 terms?
21.3- Quadratic Sequences
Question 1 : Give the name to the following sequence :
1 , 2, 4, 8, 16, 32
21.4-Special Sequences
Question 1 : Give the name to the following sequence :
1 , 1, 2, 3, 5, 8
Question : Find the next 2 terms of the following sequence :
1, 8, 27, 64,…….
21.5-Summary and Review
Question 1 : A sequence follows the following rule: After the first two terms, each term is half the sum of the previous two terms.
The 1st term is 4. The 3rd term is 9.5. Calculate the second term?
21.6-Assessment 21
Question 1 : The linear sequence starts as follows
a + 2b , a + 6b ; a + 10b ; …….. ……..
The 2nd term has value 8
The 5th term has value 44
Calculate the values of a and b?