Geometric SequencesOverview.Finding a geometric rule.

Finding the first term ‘a’Finding the common ratio ‘r’Finding the term number ‘n’

Finding a specific term eg t5

Application problems 1 2 3

Geometric Sequences

6, 8, 10, 12…

1, 5, 25, 125… 18, 15, 12, 9,…

3, 6, 12, 24…

Geometric sequences

Arithmetic sequences

Group these sequences according to type

Start

Geometric Sequences

6, 8, 10, 12…1, 5, 25, 125…

18, 15, 12, 9,… 3, 6, 12, 24…

Geometric sequences

Arithmetic sequences

Common Difference

Common Ratio

-3 -3 -3 x2 x2 x2

Start

Geometric Rule

1 nn rat

n tn

1 3

2 6

3 12

4 24

Common Ratio r = 2

Start

= a (first term)

= a x r

= a x r x r

= a x r0

= a x r x r x r

= a x r2

= a x r3

= a x r1

123 nnt

x2x2x2

tn = 3, 6, 12, 24,

a = first term

Geometric Sequences1) 6, 12, 24, 48...

2) -405, 135, -45, 15...

1 nn rat

a = 6

a = -405

r = common ratior = term 2 term 1

31

405135

2612

r

r

General Rule:

126 nnt

1

31405

n

nt

Find the rule which generates these sequences

Start

Find ‘r’

Finding a Term6, 30, 150, 750... 1 n

n rat

a = 656

30r

General Rule:

Find t10 Find ‘a’

156 nnt

General Rule:

117187505656

10

911010

tt Remember

the power is only on the 5

Find the 10th term by substituting in a = 6 and r = 5

Start

Find the first term given a geometric sequence t6 = 972, and a common ratio r = 3

Finding the first term ‘a’

Substitute in n = 6, t6 = 972 & r = 3

1 nn rat

163972 a

aa

aa

4243972

2439723972 5 Rearrange the

equation to find ‘a’

a = 4

Start

Find the common ratio ‘r’ given a geometric sequence with t8 = 10935, and a first term of 5

Finding the common ratio ‘r’

Substitute in n = 8, t8 = 10935 & a = 5

1 nn rat

Rearrange the equation to find ‘r’

7510935 r

3r

72187 r Divide by 5r7 2187 Take the 7th root

Start

Find which term of a geometric sequence is equal to 57 344 (given a first term of 14, & common ratio of 2 )

Finding the term number ‘n’

Substitute in r = 2, tn = 57344 & a = 14

1 nn rat

Rearrange the equation to find ‘n’

121457344 n

2)1(4096 LognLog

124096 n Divide by 14

124096

nLog

Log

13nUse Logs to find n

124096 nLogLog

Start

Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0.8km. Each day she has to increase her flight distance by 20% (as children become harder to find)

An Application Problem

1) Write a rule for the flight distance on any given day

Start

First term = 0.8 km

So a = 0.8A 20% increase means multiply by 1.2

So r = 1.2

12180 nn ..Flight n = day number

1 nn rat

Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0.8km. Each day she has to increase her flight distance by 20% (as children become harder to find)

An Application Problem

2) How far did Badjelly fly on the 26th day?

Start

substitute in r = 1.2

...3169.7626 Flight

2526 2.18.0 Flight

kmFlight 7626

12180 nn ..Flight

12626 2.18.0 Flight

Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0.8km. Each day she has to increase her flight distance by 20% (as children become harder to find)

An Application Problem

3) The maximum flight possible on her current broomstick is 130km. when will she first fly this distance?

Start

Substitute in a = 0.8

tn = 130 r = 1.2Term

formula1 n

n rat

2.1)1(5.1622.15.162 1

LognLog

n

12.18.0130 n

2.15.1621

LogLogn

299.271

nn

Always Round

Up!

The characters in this PowerPoint are purely fictional and are not based on any real

people either living or dead. Any coincidental resemblance to JW is unintentional and accidental.