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Sequence
ARITHMETIC SEQUENCES AND SERIES
What is an arithmetic sequence?
A sequence in which each term is found by ADDING the same number to the previous term.
4, 8, 12 , 16, 20…
+4 +4+4 +4
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
WHAT IS A GEOMETRIC SEQUENCE?
A sequence in which each term can be found by multiplying the previous term by the same number.
3, 9, 27 , 81, 243…………..
x3 x3x3 x3
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
LET’S
PRACTICE!
IS THIS AN ARITHMETIC OR
GEOMETRIC SEQUENCE?
10, 15, 20, 25, 30……
Arithmetic Sequence +5 5 is the common difference
Is this an arithmetic or geometric sequence?
2, 12, 72, 432, 2,592……
Geometric Sequence x6 6 is the common ratio
WHAT IS THE NEXT TERM IN THIS SEQUENCE?
5, 20, 80, 320 , _____
1,280
x4 x4 x4 x4
What is the next term in this sequence?
5, -1, -7 -13 , _____
-19
-6 -6 -6 -6
WHAT IS THE NEXT TERM IN THIS SEQUENCE?
-3, 6, -12, 24 , _____
-48
X-2 X-2 X-2 X-2
What is the next term in this sequence?
-400,-380,-360,-340 , ____
-320
+20 +20 +20 +20
WHAT IS THE NEXT TERM IN THIS SEQUENCE?
100, 75, 50 , 25____
0
-25 -25 -25 -25
What is the next term in this sequence?
12, -48, 192 , -768____
3,072
x-4 x-4 x-4 x-4