AnswersPrecalculusModeling with Sequences and Series

Modeling with Sequences and Series — Test Answers

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Which statement describes the sequence defined by A sub n is equal to the fraction with numerator n cubed plus 3 n and denominator n squared minus 6 n ?

A
The sequence converges to a limit of infinity .
B
The sequence diverges.
C
The sequence converges to a limit of negative infinity .
D
The sequence converges to a limit of 0 .
3

Which of the following is true regarding the given sequence? 7 over 12 comma 1 sixth comma negative 1 fourth comma negative 2 thirds

A
The sequence is not arithmetic because there is no common difference between the values of n .
B
The sequence is arithmetic because there is a common difference of 1 .
C
The sequence is arithmetic because there is a common difference of negative 5 over 12 .
D
The sequence is not arithmetic because there is no common difference between the values of A sub n .
4

Which geometric series converges?

A
1 sixth plus 1 sixth plus 1 sixth plus 1 sixth plus dot dot dot
B
1 sixth plus 2 sixths plus 4 sixths plus 8 sixths plus dot dot dot
C
6 plus 2 plus 6 ninths plus 6 over 27 plus dot dot dot
D
6 plus 12 plus 24 plus 48 plus dot dot dot
6

Which of the following is an arithmetic sequence?

A
negative 3 fourths comma negative 3 fifths comma negative 3 sixths comma negative 3 sevenths comma dot dot dot
B
1 half comma 2 comma 7 halves comma 5 comma dot dot dot
C
3 fourths comma negative 3 halves comma 3 comma negative 6 comma dot dot dot
D
negative 7 over 11 comma 6 over 11 comma negative 5 over 11 comma 4 over 11 comma dot dot dot
8

Which summation formula represents the series? 13 plus 9 plus 5 plus 1

A
the sum from n is equal to 13 to 16 of open paren n minus 4 close paren
B
the sum from n is equal to 17 to 20 of open paren n minus 4 close paren
C
the sum from n is equal to 1 to 4 of open paren negative 4 plus 17 close paren
D
the sum from n is equal to 1 to 4 of open paren negative 4 minus 15 close paren
9

What are the first three terms of a geometric sequence in which A sub 5 is equal to 25 and the common ratio is 5 ?

A
25 comma 125 comma 625
B
1 over 25 comma 1 fifth comma 1
C
1 over 25 comma 1 over 125 comma 1 over 625
D
125 comma 25 comma 5
10

What is the summation notation for the geometric series 5 plus 10 plus 20 plus 40 plus 80 ?

A
the sum from k is equal to 1 to 5 of 5
B
the sum from k is equal to 1 to 5 of 2
C
the sum from k is equal to 0 to 4 of 5
D
the sum from k is equal to 1 to 4 of 5
13

Which graph represents a geometric sequence?

A
Image with description On the coordinate plane, the x axis is marked from 0 to 10 with an interval of 1 unit and the y axis is marked from 0 to 100 with an interval of 10 units. The points (0 comma 100), (1 comma 50), (2 comma 25), (3 comma 12 point 5), and (4 comma 6 point 25) are plotted on the graph. The points are labeled on the graph with the coordinates.
B
Image with description On the coordinate plane, the x axis is marked from 0 to 10 with an interval of 1 unit and the y axis is marked from 0 to 100 with an interval of 10 units. The points (0 comma 0), (1 comma 1), (2 comma 4), (3 comma 9), (4 comma 16), (5 comma 25), (6 comma 36), (7 comma 49), (8 comma 64), and (9 comma 81) are plotted on the graph. The points are labeled on the graph with the coordinates.
C
Image with description On the coordinate plane, the x axis is marked from 0 to 10 with an interval of 1 unit and the y axis is marked from 0 to 100 with an interval of 10 units. The points (0 comma 100), (1 comma 50), and (2 comma 0) are plotted on the graph. The points are labeled on the graph with the coordinates.
D
Image with description On the coordinate plane, the x axis is marked from 0 to 10 with an interval of 1 unit and the y axis is marked from 0 to 100 with an interval of 10 units. The points (0 comma 0), (1 comma 10), (2 comma 20), (3 comma 30), (4 comma 40), (5 comma 50), (6 comma 60), (7 comma 70), (8 comma 80), and (9 comma 90) are plotted on the graph. The points are labeled on the graph with the coordinates.
14

An arithmetic series is represented by the equation cap s sub 24 is equal to the sum from k is equal to 1 to 24 of negative 6 plus 0 point 5 Which of the following is true?

A
The value of the series is equal to the value of the 1 st or 24 th numbers in the series.
B
The value of the series is between the values of the 1 st and 24 th numbers in the series.
C
The value of the series is greater than the value of the 24 th number in the series.
D
The value of the series is less than the value of the 1 st number in the series.
15

Consider the series 1 fourth plus 1 over 16 plus 1 over 64 plus 1 over 256 plus dot dot dot Which expression defines cap s sub n ?

A
cap s sub n is equal to 1 fourth to the n th power
B
cap s sub n is equal to 1 third times open paren 1 minus 1 fourth to the n th power close paren
C
cap s sub n is equal to open paren 1 minus 1 fourth to the n th power close paren
D
cap s sub n is equal to 1 third times 1 fourth to the n th power
18

Which of the following is one way the expression the sum from n is equal to 18 to 64 of open paren 1 half close paren can be rewritten using summation properties?

A
1 half times open paren the fraction with numerator 64 times 65 and denominator 2 close paren minus 1 half times open paren the fraction with numerator 19 times 20 and denominator 2 close paren
B
1 half times open paren the fraction with numerator 64 times 65 and denominator 2 close paren minus 1 half times open paren the fraction with numerator 17 times 18 and denominator 2 close paren
C
1 half times open paren the fraction with numerator 64 times 65 and denominator 2 close paren
D
1 half times open paren the fraction with numerator 46 times 47 and denominator 2 close paren
19

The relationship between women’s whole-number shoe sizes and foot lengths is an arithmetic sequence, where A sub n is the foot length in inches that corresponds to a shoe size of n A women’s size 7 fits a foot 9 and 1 third inches long, and a women’s size 12 fits a foot 11 inches long. What is the explicit formula for the arithmetic sequence? Round to the nearest hundredth, if necessary.

A
A sub n is equal to negative 5 plus 2 point 9 9 times open paren n minus 1 close paren
B
A sub n is equal to negative 17 point 9 1 plus 2 point 9 9 times open paren n minus 1 close paren
C
A sub n is equal to 7 point 3 5 plus 0 point 3 3 times open paren n minus 1 close paren
D
A sub n is equal to 7 plus 0 point 3 3 times open paren n minus 1 close paren
20

Which of the following can be used to evaluate this series? the sum from k is equal to 1 to 8 of 5

A
5 times open paren the fraction with numerator 1 minus 2 thirds to the 9th power and denominator 1 minus 2 thirds close paren
B
5 times open paren the fraction with numerator open paren 1 minus 2 thirds close paren to the 8th power and denominator 1 minus 2 thirds close paren
C
5 times open paren the fraction with numerator 1 minus 2 thirds to the 7th power and denominator 1 minus 2 thirds close paren
D
5 times open paren the fraction with numerator 1 minus 2 thirds to the 8th power and denominator 1 minus 2 thirds close paren

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