Arithmetic and Geometric Sequences

Arithmetic or Geometric and what is d or r?

100

-4, 2, -1, 1/2

This is a Geometric sequence 

Common ratio: -1/2

200

2 1/2 , 3, 3 1/2, 4, 4 1/2...

What is Arithmetic?

d=1/2

300

2, 4, 6, 8...

What is Arithmetic?

d=2

400

-2, -4, -8, -16...

What is Geometric?

r=2

500

The sequence -5, -10, -15, -20

What is what is arithmetic?

d=-5

Exponential Functions 1

100

Is the exponential function f(x)= 5^..8^x exponential growth or decay? Why?

Decay. The base is between 0 and 1. 

200

What is the y-intercept of the function y=10^.2^x

10

300

Graph the following exponential function: 

y=2(.5)^x

y-intercept =2

exponential decay

400

What is the formula for exponential growth and decay? ex: of a population

y= P(1+-r)^t

500

What is the formula for half-life?

y= a(.5)^t/h

Exponential Functions 2

100

A population of 500 bacteria triples every hour. Write an exponential equation to model this. 

y=500(3)^x

200

A colony of bacteria starts with 8000 cells and doubles every 5 days. How many bacteria will be present after 20 days? 

128000

300

A car worth $18000 depreciates by 25% each year. Find its value after 4 years. 

5695.31

400

A small town has a population of 5000 people. It is growing at a rate of 3% each year. What is the population after 10 years?

6720

500

A hospital has 100 mg of a radioactive substance with a half-life of 6 hours. How much remains after 24 hours? 

6.25 mg

Writing Equations (Geometric)

100

Write an equation for the nth term of the geometric sequences.

3, 15, 75, 375, 1875, ... 

a_n = 3*5^n-1

200

Write an equation for the nth term of the geometric sequences. 

324, 108, 36, 12, 4, ...

a_n = 324 * (1/3)^n-1

300

Write an equation for the nth term of the geometric sequences. 

1, -2, 4, -8, 16, ....

a_n=1 * (-2)^n-1

400

Write an equation for the nth term of the geometric sequences. Then find the 8th term

3, 6, 12, 24, ...

a_n= 3*(2)^n-1

a₈= 384

500

Write an equation for the nth term of the geometric sequences. Then find the 10th term

128, 64, 32, 16, 8, ...

a_n= 128(1/2)^n-1

a₁₀= 0.25

Writing Equations (Arithmetic)

100

Write an equation for the nth term of the arithmetic sequences. 

1, 4, 7, 10, 13, ...

a_n = 1 + (n - 1)3

200

Write an equation for the nth term of the arithmetic sequences. 

3, 8, 13, 18, 23, ...

a_n = 3 + (n - 1)5

300

Write an equation for the nth term of the arithmetic sequences. 

-8, -2, 4, 10, 16, ...

a_n = -8 + (n - 1)6

400

Write an equation for the nth term of the arithmetic sequences. Then find the 7th term.

-6, 1, 8, 15, 22, ...

a_n = -6 + (n - 1)7

a₇ = 36

500

Write an equation for the nth term of the arithmetic sequences. Find the 10th term

11, 4, -3, -10, -17, -24, ...

a_n = 11 + (n - 1)(-7)

a₁₀ = -52