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Sequences and series:

Arithmetic series

8.1 Sequences

LO: To be able to find the formula for the terms of a sequence

8, 11, 14, 17, …

u1 = first term

u2 = second term…

Term-to-term rule (recurrence relation – give first term in sequence and the

relationship between successive terms)

General term / nth term

5, 9, 13, 17, ….

Term-to-term rule

(recurrence relation)

General term / nth term

15, 12, 9, 6, ….

Term-to-term rule

(recurrence relation)

General term / nth term

Ignore the signs – Find the nth term.

(-1)n = -1 when n is odd

(-1)n = +1 when n is even

Do the signs of the terms alternate?

2n(-1)n

1)1( n

,...8,6,4,2

1)1( n

1)1)(82( nn

,...16,14,12,10

1)1)(112( nn

,...3,5,7,9

If the numbers go up rapidly and are not

obviously being multiplied by the same

number, the nth term could contain a

square or a cube or a quadratic.

,...81,64,27,8,1

13 )1( nn

,...25,16,9,4,1

12 )1( nn

,...8,4,2,1

12 n

Look for powers of numbers

nth term is given:

1. Find the first 4 terms

of the sequence.

nn x

2

1

2. Which term in the

sequence is

3. Express the

sequence as a

recurrence relation

1024

1

A sequence is defined by a recurrence relation of

the form

Given that M1 = 10, M2 = 20, M3 = 24, find the value

of a and the value of b and hence find M4.

baMM nn 1

Page 133 Exercise 8A

Questions 1 a, c, e

2 a, b, c and 6