Journey to the n th level

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

A few sequences…What comes next? 20, 15, 10, 5…. ….. 0, -5 term to term rule: subtract 5

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

10, 20, 30, 40, 50, 60, 70…… n = 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 n nth term = n x 10 or 10n n th term expressions

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

What is the position to term rule: 2, 4, 6, 8, 10 …. nth term = 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 700 1,000 1,800 for the last sequence (100n)

Sequences the nth term D gradeC 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 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

Questions to try Page 68 Exercise 7A Questions 1 a, c, e & g Question 2 a, c, e & g Question 3 Question 4 Question 6 Finished? CHECK your answers with a friend and on page 282 Additional challenges available! Need help? Just ask

more complicated…. 5, 8, 11, 14, 17, 20 ….. +3 common difference is nth term =3n n = 0 1 st 2 nd 3 rd 4 th 5 th 6 th 2,

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 n= 0 1 st 2 nd 3 rd 4 th 5 th 1, Clip 112 Finding The Nth Term.avi

Extension: h)1, 9, 17, 25, 33.. i)-2, 8, 18, 28, 38.. j)-2, -4, -6, -8, k)1, 4, 9, 16, 25.. l)3, 6, 11, 18, 27.. a)3, 5, 7, 9, 11, 13…. b)12, 20, 28, 36, 44…. c)19, 29, 39, 49, 59…. d)7, 10, 13, 16, 19…. e)14, 20, 26, 32, 38…. f)55, 60, 65, 70, 75… g)8, 17, 26, 35, 44…. 2n+1 8n+4 10n+9 3n+4 6n+8 5n+50 9n-1 8n-7 10n-12 -2n n2n2 n 2 +2

Questions to try Page 71 Exercise 7B Questions 1 a, c, e & g Question 3 a, c & e Question 4 Question 5 Finished? CHECK your answers with a friend and on page 281 Additional challenges available! Need help? Just ask

What sequence rule would the pattern of matchsticks follow: 2n , 3, 5, 7…

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 20n + 350or 0.20n p x minutes + call charge= Total cost 0.20 x = £27.50