The document contains information about arithmetic and geometric sequences. It defines an arithmetic sequence as one where each term is found by adding the same number to the previous term, called the common difference. A geometric sequence is one where each term is found by multiplying the previous term by the same number, called the common ratio. Examples are worked through and questions are asked about finding the next term in various sequences.

1. Examine the following lists below
and group the lists into three:
-2,-3,-4,-5,-6
2,7,8,11,19
3,6,9,12,15
1,3,9,27,81
0,1.1,4,5,7.7

2. What is an arithmetic
sequence?
A sequence in which
each term is found by
ADDING the same
number to the previous
term.
4, +4 8,+4 12 +4 16,+4 20…………..
,

3. What is the common
difference?
The difference between
each number. This
determines what is added to
each previous number to
obtain the next number.
4, 8, 12, 16, 20…………..
4 is the common difference

4. What is a geometric
sequence?
A sequence in which
each term can be found
by multiplying the
previous term by the
same number.
3,x3 9,x3 27x3 81, 243…………..
, x3

5. What is the common
ratio?
The number used to multiply
by each previous number to
obtain the next number.
2, 8, 32, 128, 512…………..
4 is the common ratio

6. Let’s
Practice!

7. Is this an arithmetic or
geometric sequence?
10, 15, 20, 25, 30……
Arithmetic Sequence
+5
5 is the common difference

8. Is this an arithmetic or
geometric sequence?
2, 12, 72, 432, 2,592……
Geometric Sequence
x6
6 is the common ratio

9. What is the next term in
this sequence?
x4 x4 x4 x4
5, 20, 80, 320 , _____
1,280

10. What is the next term in
this sequence?
-6 -6 -6 -6
5, -1, -7 -13 , _____
-19

11. What is the next term in
this sequence?
X-2 X-2 X-2 X-2
-3, 6, -12, 24 , _____
-48

12. What is the next term in
this sequence?
+20 +20 +20 +20
-400,-380,-360,-340 , ____
-320

13. What is the next term in
this sequence?
-25 -25 -25 -25
100, 75, 50 , 25____
0

14. What is the next term in
this sequence?
x-4 x-4 x-4 x-4
12, -48, 192 , -768____
3,072