Unit 2 Review

Sequences

100

What is the pattern of the following sequence and find the next three terms: 3,-9,27,-81,... 

r=-3 

243,-729,2187

200

What is the explicit formula for the following sequence: 1,4,7,10,...

a(n)=1+(n-1)(3)

300

Write the explicit formula for the following sequence and find the next three terms: 6,1,-4,-9,...

a(n)=6+(n-1)(-5)

-14,-19,-24

400

Write an explicit formula and find the 12th term of the sequence: 2,4,8,16,32,...

a(n)=2(2)^n-1

a(12)=4096

500

Find the 30th term of the sequence: 

3,-3,-9,-15,...

a(30)=171

Inverse

100

Find the inverse of 

g(x) = 3x+2

g^-1(x)=x-2/3

200

Find the inverse of g(x) = -8x+16 

g^-1(x) = 1/8x - 2 

300

g(x) = 2/3x - 5 

g^-1(x) = 3/2x  + 15/2 

400

h(x) = x^2 + 5 

h^-1(x)= sqrt(x-5) 

500

Are these two functions inverses of eachother 

f(x) = -4x + 8 

g(x) = -1/4x + 2 

Yes they are inverses of eachother 

Series

100

8, 20, 32, 44, … 𝑛 = 10

Find the sum 

S(10) = 620 

200

𝑎1 = 3, 𝑑 = 2, 𝑛 = 12

S(12) = 168  

300

𝑎1 = 100, 𝑑 = −5, 𝑛 = 8 

S(9)= 660 

400

Find the Sum of the first 7 terms of the following sequence:  4 + 8 + 16 + 32 + ⋯

S(7) = 508

500

How many terms of the arithmetic sequence 15, 12, 9,…must be added to get −39?

𝑛 = 13

Exponential Growth/Decay

100

y=100(1.25)^x

a)What is the initial Value?

b)Does the function represent growth or decay? 

c)What is the rate of growth or decay?

a)100

b)growth

c) 25%

200

y=5575(.65)^x

a)What is the initial Value?

b)Does the function represent growth or decay? 

c)What is the rate of growth or decay?

a) 5575

b)Decay

c)35%

300

The price of a car that was bought for $10,000 and has depreciated 10% yearly. Find the price of the car 8 years later.

y= 4304.67

400

The equation for the price of a baseball card that was bought for 5 dollars and has appreciated 5% yearly. Find the value of the card 25 years later.

y=16.93

500

A town of 3200, grows at a rate of 25% every year. Find the size of the city in 10 years.

y=29802.32