Journey to the nth level

A few sequences… What comes next?

9, 13, 17, 21….

….. 25, 29term to term rule: add 4

A few sequences…What comes next?

20, 15, 10, 5….

….. 0, -5term to term rule: subtract 5

A few sequences…What comes next?

1, 10, 100, 1000….

….. 10,000, 100,000term to term rule: x 10

10, 20, 30, 40, 50, 60, 70……n = 1st 2nd 3rd 4th 5th 6th 7th

The position to term rule is: whichever term I’m

interested in X 10nnth term = n x 10

or 10n

nth term expressions

4, 8, 12, 16, 20, 24, 28……

The position to term rule is: whichever term I’m

interested in X 4nnth term = n x 4

4n

n= 1st 2nd 3rd 4th 5th 6th 7th

nth 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 7th term?What’s the 10th term?What’s the 18th term?

n x 2 = 2n

700

1,0001,800

for the last sequence (100n)

Sequencesthe nth term

D grade C gradegenerate 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 tryPage 68 Exercise 7AQuestions 1 a, c, e & gQuestion 2 a, c, e & gQuestion 3 Question 4Question 6Finished? CHECK your answers with a friend and on page 282Additional challenges available!

Need help? Just ask

more complicated….

5, 8, 11, 14, 17, 20 …..

+3 +3 +3 +3 +3 common difference is 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

nth term = 3n + 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

+ 2

-3

n = 0 1st 2nd 3rd 4th 5th 6th

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

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

+ 1

n= 0 1st 2nd 3rd 4th 5th

1,

Clip 112 Finding The Nth Term.avi

Questions to try

Page 71 Exercise 7BQuestions 1 a, c, e & gQuestion 3 a, c & eQuestion 4Question 5Finished? CHECK your answers with a friend and on page 281Additional challenges available!

Need help? Just ask

What sequence rule would the pattern of matchsticks follow:

2n + 1

+2-2

1, 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

Real Life Example:

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 + 350 or 0.20n + 3.50

20p x minutes + call charge = Total cost

0.20 x 120 + 3.50 = £27.50