1. Geometric Sequences Overview. Finding a geometric rule.
Finding a specific term eg t5
Finding the first term ‘a’
Finding the common ratio ‘r’
Finding the term number ‘n’
Application problems 1 2 3

2. Geometric Sequences Geometric sequences Arithmetic sequences
Start
Geometric Sequences
Common Difference
6, 8, 10, 12…
3, 6, 12, 24…
1, 5, 25, 125…
Common Ratio
18, 15, 12, 9,…
Group these sequences according to type
Geometric sequences
Arithmetic sequences

3. Geometric Sequences x2 -3 Geometric sequences Arithmetic sequences
Start
Geometric Sequences
Common Difference
Common Ratio x2 -3
3, 6, 12, 24…
18, 15, 12, 9,…
1, 5, 25, 125…
6, 8, 10, 12…
Geometric sequences
Arithmetic sequences

4. Geometric Rule x2 tn = 3, 6, 12, 24, n tn 3 6 12 24 Common Ratio r = 2
Start
Geometric Rule
tn = 3, 6, 12, 24,
n tn 3 6 12 24
Common Ratio r = 2
= a (first term)
= a x r0 x2
= a x r
= a x r1
= a x r x r
= a x r2
= a x r x r x r
= a x r3

5. Geometric Example A Start 1) 6, 12, 24, 48... a = 6
2) -405, 135, -45, 15...
a = 6
a = -405
Find the rule which generates these sequences
General Rule:
r = common ratio
r = term 2
term 1
a = first term

6. Finding a ‘Term’ Find t10 6, 30, 150, 750... Start General Rule:
Find ‘a’
a = 6
Find ‘r’
General Rule:
Find the 10th term by substituting in a = 6 and r = 5
Remember the power is only on the 5

7. Finding the first term ‘a’
Start
Find the first term given a geometric sequence t6 = 972, and a common ratio r = 3
Substitute in n = 6, t6 = 972 & r = 3
Rearrange the equation to find ‘a’
a = 4

8. Finding the common ratio ‘r’
Start
Find the common ratio ‘r’ given a geometric sequence with t8 = 10935, and a first term of 5
Substitute in n = 8,
t8 = & a = 5
Rearrange the equation to find ‘r’
Divide by 5
Take the 7th root

9. Finding the term number ‘n’
Start
Find which term of a geometric sequence is equal to (given a first term of 14, & common ratio of 2 )
Substitute in r = 2,
tn = & a = 14
Rearrange the equation to find ‘n’
Divide by 14
Use Logs to find n

10. An Application Problem A
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)
First term = 0.8 km
So a = 0.8
A 20% increase means multiply by 1.2
So r = 1.2
1) Write a rule for the flight distance on any given day
n = day number

11. An Application Problem B
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)
2) How far did Badjelly fly on the 26th day?
substitute in r = 1.2

12. An Application Problem C
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)
Always Round Up!
3) The maximum flight possible on her current broomstick is 130km. when will she first fly this distance?
Substitute in a = 0.8
tn = 130 r = 1.2
Term formula

13. 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.