Learning Intention Describe number sequences A number pattern

Learning Intention – Describe number sequences

A number pattern which increases (or decreases) by the same amount each time is called a linear sequence. The amount it increases or decreases by is known as the common difference. Today we are going to be describing the numbers in a sequence and finding the next number using a formula.

Look at the number sequence, 3 5 7 9 The sequence increase by steps of 2. The first term (first number) is 3 The fourth term is 9 How do we find the fifth and tenth term? We need to count in steps of 2. Write the number sequence out finding the fifth and tenth term in the sequence.

Describe Linear Sequences Here is a linear sequence: 3 The 1 st term is: 3 The 4 th term is: 9 The step is: 2 The 5 th term will be: The 10 th term will be: 11 21 5 7 9

Describe Linear Sequences Here is a linear sequence: 2 The 1 st term is: 2 The 4 th term is: 17 The step is: 5 The 5 th term will be: The 10 th term will be: 22 47 7 12 17

Describe Linear Sequences Here is a linear sequence: 2 The step is: 5 8 11 3 The first term is: The first term = 2 the step – 1 As the linear sequence increase by steps of 3 each time her but the number sequences does not begin with a 3, the formula to find the first number in the sequence is the step subtract 1. The step is 3 then subtract 1.

Describe Linear Sequences Here is a linear sequence: 6 The step is: 10 14 18 4 The first term is: The first term = 6 the step + 2

To generate linear number sequences… You need to use the formula you are given to find the next number in the sequence. Look at the last number of the sequence, in this case it is 13. Use the formula: 2 n + 1 when n = 13? The calculation is 13 x 2 + 1 So the next number in the sequence is 27

Generate Linear Number Sequences The formula 2 n + 1 can be used to calculate the value of these terms in this sequence: 3 5 7 9 11 13 What is 2 n + 1 when n = 13? 27 What is 2 n + 1 when n = 50? 101

Generate Linear Number Sequences The formula n - 3 can be used to calculate the value of these terms in this sequence: -2 -1 0 1 2 3 What is n - 3 when n = 17? 14 What is n - 3 when n = 70? 67

Generate Linear Number Sequences The formula 6 n - 5 can be used to calculate the value of these terms in this sequence: 1 7 13 19 25 31 What is 6 n - 5 when n = 15? 85 What is 6 n - 5 when n = 90? 535

Generate Linear Number Sequences The formula 7 n + 4 can be used to calculate the value of these terms in this sequence: 11 18 25 32 39 What is 7 n + 4 when n = 8? 60 What is 6 n + 4 when n = 30? 184

Generate Linear Sequences The following linear sequence shows the first four terms. 4 7 10 13 What is the 10 th term and the 20 th term? 10 th term = 31 20 th term = 61 Write the formula for the nth term: 3 n + 1

Generate Linear Sequences The following linear sequence shows the first four terms. 1 5 9 13 What is the 10 th term and the 20 th term? 10 th term = 37 20 th term = 77 Write the formula for the nth term: 4 n - 3