GPS GeometryDay 72 (11-20-13)

UNIT QUESTION: How is a geometric sequence like an exponential function?Standard: MM2A2, MM2A3

Today’s Question:How is a geometric sequence like an exponential function?Standard: MM2A2, MM2A3

Geometric Sequences

Geometric Sequences

• In geometric sequences, you multiply by a common ratio each time.

• 1, 2, 4, 8, 16, ... multiply by 2• 27, 9, 3, 1, 1/3, ...

Divide by 3 which means multiply by 1/3

Geometric Sequences• Find the 8th term of the sequence:

2,6,18,…Determine the pattern:Multiply by 3 (known as the common

ratio)Write the new sequence:2,6,18,54,162,486,1458,4374So the 8th term is 4374.

Geometric Sequences

• Again, use a formula to find large numbers.•         an = a1 • (r)n-1 • an = The term you want• a1 = The first term• r = The common ration• n = The number of the term you want

Geometric Sequences

• Find the 10th term of the sequence :

4,8,16,…

an = a1 • (r)n-1

• a1 = 4

• r = 2

• n = 10

Geometric Sequences

an = a1 • (r)n-1

a10 = 4 • (2)10-1

a10 = 4 • (2)9

a10 = 4 • 512

a10 = 2048

Geometric Sequences

• Find the 6th term of the sequence :

8,-4,2 ,…

an = a1 • (r)n-1

• a1 = 8

• r = ???

• n = 6

Geometric Sequences

• Find the ninth term of a sequence if a3 = 63 and r = -3a1= ?n= 9r = -3a9 = ?There are 2 unknowns so you must…

Geometric Sequences

• First find a1. • Use the sequences formula substituting a3 in

for an.  a3 = 63• a3 = a1 • (-3)3-1 • 63 = a1 • (-3)2

• 63= a1 • 9• 7 = a1

Geometric Sequences

• Now that you know t1, substitute again to find tn.

an = a1 • (r)n-1

a9 = 7 • (-3)9-1

a9 = 7 • (-3)8

a9 = 7 • 6561

a9 = 45927

Geometric Sequences

• Find the eighth term of a sequence if a2 = 2 and a6 = 512

Application

A 5-day rain caused the Olentagy River to rise. After the first day, the river rose one inch. Each day the rise in the river tripled. How much has the river risen after 5 days?

Class work

Coach Book Page 93 and 94

Homework

Page 145 #1-17 (odd),

skip graph on 7 & 9