Journey to the nth level A few sequences

Journey to the nth 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, 100, 1000…. …. . 10, 000, 100, 000 term to term rule: x 10

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

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

What is the position to term rule: 2, 4, 6, 8, 10 …. nth term = n x 2 = 2 n 100, 200, 300, 400…. nth term = 100 n for the last sequence (100 n) What’s the 7 th term? 700 What’s the 10 th term? 1, 000 What’s the 18 th term? 1, 800

Sequences the nth term D grade C grade generate terms of a linear sequence using term-toterm and position-to-term rules generate terms of a sequence using term-to -term and position-toterm rules write an expression for the generate sequences nth term of a simple from practical contexts arithmetic sequence, and write and justify an expression to describe the nth term of an arithmetic sequence

Questions to try Page 68 Exercise 7 A Need help? Just ask 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!

more complicated…. n=0 1 st 2 nd 3 rd 4 th 5 th 6 th 2, 5, 8, 11, 14, 17, 20 …. . -3 1 2 +3 3 4 +3 +3 common difference is 3 5 6 7 8 9 10 11 12 13 14 15 16 17 +2 1 2 3 4 nth term = 3 n + 2

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, 6, 11, 16, 21, 26… Step 1: Common difference? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Step 2: How has the table been shifted? +1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 nth term = 5 n + 1 Clip 112 Finding The Nth Term. avi

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

1, -2 3, 5, +2 What sequence rule would the pattern of matchsticks follow: 2 n + 1 7…

You own a taxi company that charges as follows: • £ 3. 50 for calling the cab • 20 p 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 20 n + 350 20 p or 0. 20 n + 3. 50 x minutes + call charge 0. 20 x 120 + 3. 50 = Total cost = £ 27. 50