Algebra 1B Unit 2 Lesson 6

James deposited some money into a savings account to save for a motorcycle. Based on the interest rate of the account, he estimates that his money will grow according to the following table. (1, 1428) (2,1457) (3,1486) (4,1516) (5,1546) The values follow a geometric sequence. What is the common ratio of the sequence? Enter your answer as a decimal rounded to two decimal places, if necessary, like this: 42.53

1.02

Which statements about geometric sequences are true? There is more than one correct answer. Select all that apply.

Geometric sequences have a common ratio between terms. Geometric sequences are restricted to the domain of natural numbers.

Use the following partial table of values for a geometric sequence to answer the question. (1,196) (2,2744) (3,38416) (4,537824) (5,7529536) (6,105413504) Which statements are true for calculating the common ratio, r, based on the table of values? There is more than one correct answer choice. Select all that apply.

When the coordinates (5,7529536) and (6,105413504) are considered, r=105,413,504/7,529,536=14. When the coordinates (2,2744) and (3,38416) are considered, r=38,416/2744=14. When the coordinates (1,196) and (2,2744) are considered, r=2744/196=14.

Which statement describes a geometric sequence?

a sequence of numbers in which each term is produced by multiplying the previous term by a common ratio

Which recursive formula represents the sequence {1,2,4,8,16,...}?

a1=1 and an=2an−1

Two terms in a geometric sequence are a3=729 and a4=243 What is the first term of the sequence, and what is the recursive rule that describes the sequence?

a1=6,561; an=1/3an−1

The popularity of a new music artist has been growing exponentially each week. The table shows how many song downloads the artist has had so far. (1,75) (2,450) (3,2700) (4,16200) Which of the following is a recursive formula that represents the information in the table?

a1=75 and an=a(n−1)⋅6

A value in a sequence is 2 times the previous value, like this: {8,16,32,64}. How would this sequence be represented as a recursive equation?

a1=8 and an=2an−1

Study the geometric sequence {−4,−84,−1764,−37044,...}. What is the explicit formula for the sequence?

an=(−4)(21)(n−1)

Use the sequence {0.3,0.03,0.003,0.003,...} to answer the question. What is the explicit rule that describes the sequence?

an=0.3(0.1)(n−1)

The common ratio of a sequence is 3. Two terms in the sequence are a4=3 and a8=243. What is the explicit rule that describes this sequence?

an=1/9(3)n−1

Two values of a geometric sequence are a2=33 and a3=363 What is the explicit formula for this sequence?

an=3⋅11(n−1)

A geometric sequence has a common ratio of 2 and the 12th term is −12,288 What is the explicit rule that describes this sequence?

an=−6⋅2(n−1)

Consider the terms in the sequence: {4,32,256,2048,16,384,...} Match each expression with the correct answer.

common ratio of the sequence- r=8 first term in the sequence- a1=4 recursive rule in function notation that describes the sequence- f(n)= 8f(n-1)

Use the following partial table of values of a geometric sequence to answer the question. (1,0.625) (2, 0.25) (3,1) (4,4) (5,16) (6,64)

f(n)=0.0625(4)n−1

Use the following partial table of values of a geometric sequence to answer the question. (1,2) (2,4) (3,8) (4,16) (5,32) (6,64) Which function rule could represent this sequence?

f(n)=2(2)n−1, where n is a natural number.

The points on this graph represent a geometric sequence. https://assets.learnosity.com/organisations/625/asset/media/1155265 What is the explicit formula, in function notation, that could produce the sequence?

f(n)=4(1/2)n−1

Consider the terms in the sequence: {13,19,127,...} Match each expression with its correct answer.

first term in the sequence- a1= 1/3 recursive rule that describes the sequence- an=1/3an-1 common ratio of the sequence- r=1/3

The common ratio of a sequence is 1/2. Two terms in the sequence are a5=1 and a8=1/8. Match each expression with the correct answer.

first term in the sequence- a1=16 recursive rule that describes the sequence- an=1/2an-1

Which answer represents a geometric sequence?

{1,3,9,27,...}

Which answers are geometric sequences? There is more than one correct answer. Select all that apply.

{2,−10,50,−250,...} {1,−1,1,−1,1,...} {108,36,12,4,...}

Which answer represents a geometric sequence?

{−1008,−504,−252,−126,...}