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