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Sequence and Exponent Quest Review

Side A

Question 1

The explicit formula of a sequence is given by 𝑎(𝑛) = 6𝑛 − 2

(a) Find the 150th term in the sequence

(b) How much does the sequence increase by?

(c) Find the y-intercept

Question 2

The recursive formula of a sequence is given by 𝑎1 = 2 and 𝑎𝑛 = 3 ∙ 𝑎𝑛−1 + 1. Find the value of 𝑎6

Question 3

An arithmetic sequence is defined by the list −3, 5, 13, 21, 29 where 𝑎(1) = −3.

(a) Find the value of 𝑎(9) (b) Create an explicit definition for this sequence

Question 4

The function 𝑔(𝑥) is defined by the table below. Find the average rate of change within the interval −2 ≤ 𝑥 ≤

1. Round to the nearest hundredth if necessary.

𝑥 −2 −1 0 1 2 3

𝑔(𝑥) 1 3 9 27 81 243

Question 5

The population of pigeons in Vermillion City was 20. Each day, the population quadrupled.

(a) Create an equation 𝑓(𝑥) = for the number of pigeons on day 𝑥

(b) Find the number of pigeons in Vermillion City after 1 week.

Question 6

The function ℎ(𝑥) is defined by ℎ(𝑥) = 81(3)𝑥. Evaluate ℎ(−3) and find the y-intercept of ℎ(𝑥)

Question 7

The average puppy is born at 4 lbs. Each year, the average puppy grows 3% in weight.

(a) Find the weight of an average puppy after its first birthday.

(b) Create an equation for the weight of an average puppy on day 𝑛, assuming puppies grow by the same

percentage each year.

Question 8

Gandalf created a geometric sequence defined by the recursive formula 𝑎(1) = 108 and 𝑎(𝑛) = 𝑎(𝑛 − 1) ∙1

3

(a) List out 5 terms in this sequence

(b) Create an explicit definition for this geometric sequence

Side B

Question 1

The function 𝑘(𝑥) is defined by the formula 𝑘(𝑥) = 64(8)𝑥

(a) Evaluate 𝑘(−3) (b) Find the y-intercept

Question 2

The sequence 𝑎(𝑛) is defined recursively as 𝑎(1) = 3 and 𝑎(𝑛) = 2 ∙ 𝑎(𝑛 − 1) − 1. Find the value of 𝑎(5)

Question 3

The number of assignments Mr. Peralta assigns grows exponentially. It began with two assignments. The

number of assignments doubled each month.

(a) Create an equation 𝑦 = for the number of assignments given on month 𝑥

(b) Find the number of assignments given on the fourth month of school

Question 4

The U.S. population is growing at a rate of 2% each year. Currently, the U.S. population is 315,000,000.

(a) Find the U.S. population next year.

(b) Create an equation for the population in the U.S. x years from today.

Question 5

An arithmetic sequence is defined by the following list of numbers, where 𝑎(1) = 12

12, 7, 2, −3,−8

(a) Find the value of 𝑎(6) (b) Create an explicit definition for this geometric sequence

Question 6

An arithmetic sequence is defined by the explicit formula 𝑎𝑛 = −3𝑛 + 14

(a) Find the 75th element in this sequence

(b) How much does the sequence change by? How do you know?

Question 7

A sequence 𝑓(𝑥) is defined is below, where 𝑓(1) = 2. Find the average rate of change defined in the interval

2 ≤ 𝑥 ≤ 6

2, 4, 8, 16, 32, 64, 128

Question 8

Mary created a geometric sequence defined by the recursive formula 𝑎(1) =1

2 and 𝑎(𝑛) = 𝑎(𝑛 − 1) ∙ 4

(a) List 5 terms in this sequence

(b) Create an explicit definition for this geometric sequence