Geometric Sequences

Multiple Choice Equations

200

If the equation to determine the n^th term in an equation is g_n=150(15)¹⁰,

What is the value of r?

A) 15

B) 150 

C) 1.5

D) 437

A

400

If the equation to determine the n^th term in an equation is g_n=5(9)¹⁶,

What is the value of r?

A) n

B) 5

C) 9

D) 16

C

600

Is the following sequence a geometric sequence?

[²/₃, ⁴/₃, 2,...]

A) Yes

B) No

B

800

What is the sum of the first 5 terms of the geometric sequence?

[2,6,18]

A) 392

B) 242

C) 150

D) 450

B

1000

If the equation to determine the n^th term in an equation is g_n=5(10)¹⁵,

Given the first term in the sequence is 5, what is the value of r*(n-1)

A) 5

B) 10 

C) 150

D) 15

C

Variables

200

The n^th term in a geometric sequence

g_n

400

the common ratio 

(ratio between succeeding numbers)

r

600

The original term in a geometric sequence

g₀

800

DAILY DOUBLE!!! 

The equation to determine the n^th term in a geometric sequence

g_n=g_k(r)^(n-k)

1000

the y-value of the sample term

k

Equation Set-up

200

Answer the question using the following sequence: 1,2,4,8,32 ...

Create an equation using the first term to determine the 56^th term.

g₅₆= 1(2)^(56-1)

400

Answer the question using the following sequence:

 3, 9, 27, 81, 243, ...

Create an equation using the first term to determine the 100^th term.

g₁₀₀=3(3)^(100-1)

600

Answer the question using the following sequence:

[.66, 1.33, 2.66, 5.32,...]

Create an equation using the first term to determine the 37^th term.

g₃₇=0.66(2)^(37-1)

800

Answer the question using the following sequence:

[14, 84, 504...]

Create an equation using the second term to determine the 5^th term.

g₅=84(6)^(5-2)

1000

Answer the question using the following sequence: 

[0.3125, 2, 12.8...] 

Create an equation using the third term to determine the 34th term.

g₃₄=12.8(6.4)^(34-3)

Calculator Skills

200

g₀=5

r=5

What is g₂?

125

400

g₁=16

r=1.4

What is g₅?

85.05

600

g₀=3

r=3

What is g₄

243

800

g₁=92

r=.5

What is g₀?

184

1000

g₁₂=92

r=.9

What is g₀?

325.75

Word Problems

200

A bacteria population doubles in size every hour. If its initial population is 100, how many will there be after 4 hours?

1600

400

A population of rabbits doubles in a forest every year. If the population starts at 200 rabbits, how many rabbits will there be after 10 years?

204,800 rabbits

600

If a car worth $50,000 loses 12% of its value every year, what is the value of r?

r=0.88

800

A town's population increases 5% every year. If the initial population of the town is 1000 people, how many people will live there after 40 years?

Round to the nearest whole number.

7040 people

1000

If a car worth $25,000 loses 12% of its value every year, then what is its value 5 years after it was bought?

$13193.30