A few sequences… 9, 13, 17, 21…. ….. 25, 29 term to term rule: add 4

A few sequences… 20, 15, 10, 5…. ….. 0, -5 term to term rule: minus 5

A few sequences… 1, 10, 100, 1000…. ….. 10,000, 100,000 term to term rule: x 10

A few sequences… 88, 44, 22, 11…. ….. 5.5, 2.75 term to term rule: half

Sequences the nth term Level 6 - D gradeC / DLevel 7 - C grade generate terms of a linear sequence using term-to- term and position-to-term rules generate terms of a sequence using term- to-term and position-to- term rules justify generalisations for the nth term of linear and quadratic sequences write an expression for the nth term of a simple arithmetic sequence, generate sequences from practical contexts and write and justify an expression to describe the nth term of an arithmetic sequence

10, 20, 30, 40, 50, 60, 70…… 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th The position to term rule is: whichever term I’m interested in X 10

4, 8, 12, 16, 20, 24, 28…… 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th The position to term rule is: whichever term I’m interested in X 4 n nth term = n x 4

What is the position to term rule: 2, 4, 6, 8, 10 ….nth term = 6, 12, 18, 24 ….nth term =6n 5, 10, 15, 20, 25….nth term =5n 100, 200, 300, 400….nth term =100n What’s the 7 th term? What’s the 10 th term? What’s the 18 th term? n x 2= 2n ,800

more complicated…. 5, 8, 11, 14, 17, 20 ….. +3 common difference is nth term =3n

6, 11, 16, 21, 26… Step 1: Common difference? nth term = 5n Step 2: How has the table been shifted? + 1 To work out the rule for the nth term of a sequence

!! Extension: h)1, 9, 17, 25, 33…. i)-2, 8, 18, 28, 38…. j)-2, -4, -6, -8, -10… k)1, 4, 9, 16, 25…. l)3, 6, 11, 18, 27…. !!

You own a taxi company that charges as follows: £3.50 for calling the cab 20p for every minute of journey time 1.Work out a formula for the cost of a journey that’s n minutes long 2.Use your formula to cost a journey of 2 hours

What pattern of matchsticks would follow this sequence rule: 4n + 2

Sequences the nth term Level 6 - D gradeC / DLevel 7 - C grade generate terms of a linear sequence using term-to- term and position-to-term rules generate terms of a sequence using term- to-term and position-to- term rules justify generalisations for the nth term of linear and quadratic sequences use expressions to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the context generate sequences from practical contexts and write and justify an expression to describe the nth term of an arithmetic sequence

Extension work T(n) = n 2 T(n) = 3n 2 + n T(n) = 4n 2 + n – 1 For each of these sequences work out the first five terms What is the first difference? What is the second difference? Is there a way of predicting the second difference?