Question 1

Find the indicated term(s) of the given sequence.
-The first five terms of the sequence $a _ { n } = \frac { ( - 1 ) ^ { n } } { n ^ { 2 } - 3 }$

Accepted Answer

A)  $- \frac { 1 } { 3 } , \frac { 1 } { 2 } , 1 , - \frac { 1 } { 6 } , \frac { 1 } { 13 }$ 
B)  $\frac { 1 } { 2 } , 1 , - \frac { 1 } { 6 } , \frac { 1 } { 13 } , \frac { 1 } { 22 }$ 
C)  $- \frac { 1 } { 2 } , - 1 , \frac { 1 } { 6 } , - \frac { 1 } { 13 } , \frac { 1 } { 22 }$ 
D)  $\frac { 1 } { 2 } , 1 , - \frac { 1 } { 6 } , \frac { 1 } { 13 } , - \frac { 1 } { 22 }$ 
A)  $- \frac { 1 } { 3 } , \frac { 1 } { 2 } , 1 , - \frac { 1 } { 6 } , \frac { 1 } { 13 }$ 
B)  $\frac { 1 } { 2 } , 1 , - \frac { 1 } { 6 } , \frac { 1 } { 13 } , \frac { 1 } { 22 }$ 
C)  $- \frac { 1 } { 2 } , - 1 , \frac { 1 } { 6 } , - \frac { 1 } { 13 } , \frac { 1 } { 22 }$ 
D)  $\frac { 1 } { 2 } , 1 , - \frac { 1 } { 6 } , \frac { 1 } { 13 } , - \frac { 1 } { 22 }$

Question 2

Find the indicated term of the sequence.
-The ninth term of the arithmetic sequence $23,17,11 , \ldots$

Accepted Answer

A)  71 
B)  $- 48$ 
C)  $- 31$ 
D)  $- 25$ 
A)  71 
B)  $- 48$ 
C)  $- 31$ 
D)  $- 25$

Question 3

Write the first five terms of the sequence whose general term is given.
-$a _ { n } = ( - 2 ) ^ { n }$

Accepted Answer

A)  $2,4 , - 8,16 , - 32$ 
B)  $- 2 , - 4 , - 8 , - 16 , - 32$ 
C)  $- 2,4 , - 8,16 , - 32$ 
D)  $2 , - 4 , - 8 , - 16 , - 32$ 
A)  $2,4 , - 8,16 , - 32$ 
B)  $- 2 , - 4 , - 8 , - 16 , - 32$ 
C)  $- 2,4 , - 8,16 , - 32$ 
D)  $2 , - 4 , - 8 , - 16 , - 32$

Question 4

Evaluate the expression.
-$\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 5 i }$

Accepted Answer

A)  $\frac { 11 } { 30 }$ 
B)  $\frac { 5 } { 12 }$ 
C)  $\frac { 1 } { 20 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $\frac { 11 } { 30 }$ 
B)  $\frac { 5 } { 12 }$ 
C)  $\frac { 1 } { 20 }$ 
D)  $\frac { 1 } { 4 }$

Question 5

Solve the problem.
-The number of birds born each year at the local zoo forms a sequence whose general term is $a _ { n } = ( n + 9 ) ( n - 1 )$. Find the number of birds born in the fourth year, and find the total number of birds born in the first four years.

Accepted Answer

A)  39 birds; 84 birds 
B)  24 birds; 45 birds 
C)  39 birds; 74 birds 
D)  24 birds; 35 birds 
A)  39 birds; 84 birds 
B)  24 birds; 45 birds 
C)  39 birds; 74 birds 
D)  24 birds; 35 birds

Question 6

Evaluate the expression.
-$\sum _ { i = 2 } ^ { 4 } i ( i - 5 )$

Accepted Answer

A)  $- 20$ 
B)  3 
C)  $- 10$ 
D)  $- 16$ 
A)  $- 20$ 
B)  3 
C)  $- 10$ 
D)  $- 16$

Question 7

Given are the first three terms of a sequence that is arithmetic. Find a1 and d.
-$- 14 , - 17 , - 20$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = - 14 ; \mathrm { d } = 9$ 
B)  $\mathrm { a } _ { 1 } = - 14 ; \mathrm { d } = - 6$ 
C)  $a _ { 1 } = - 14 ; d = - 3$ 
D)  $\mathrm { a } _ { 1 } = - 14 ; \mathrm { d } = - 9$ 
A)  $\mathrm { a } _ { 1 } = - 14 ; \mathrm { d } = 9$ 
B)  $\mathrm { a } _ { 1 } = - 14 ; \mathrm { d } = - 6$ 
C)  $a _ { 1 } = - 14 ; d = - 3$ 
D)  $\mathrm { a } _ { 1 } = - 14 ; \mathrm { d } = - 9$

Question 8

Use the binomial formula to expand the binomial.
-$( g - 2 h ) ^ { 3 }$

Accepted Answer

A)  $g ^ { 3 } - 6 g ^ { 2 } h + 12 g h ^ { 2 } - 8 h ^ { 3 }$ 
B)  $g ^ { 3 } + 6 g ^ { 2 } h - 12 g h ^ { 2 } + 8 h ^ { 3 }$ 
C)  $g ^ { 3 } - 8 g ^ { 2 } h + 12 g h ^ { 2 } - 6 h ^ { 3 }$ 
D)  $g ^ { 3 } - 6 g h + 12 g h ^ { 2 } - 8 h ^ { 3 }$ 
A)  $g ^ { 3 } - 6 g ^ { 2 } h + 12 g h ^ { 2 } - 8 h ^ { 3 }$ 
B)  $g ^ { 3 } + 6 g ^ { 2 } h - 12 g h ^ { 2 } + 8 h ^ { 3 }$ 
C)  $g ^ { 3 } - 8 g ^ { 2 } h + 12 g h ^ { 2 } - 6 h ^ { 3 }$ 
D)  $g ^ { 3 } - 6 g h + 12 g h ^ { 2 } - 8 h ^ { 3 }$

Question 9

Write the first five terms of the sequence whose general term is given.
-$a _ { n } = \frac { n + 1 } { 2 n - 1 }$

Accepted Answer

A)  $2 , - 1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 2 } { 3 }$ 
B)  $- 2 , - 1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , - \frac { 2 } { 3 }$ 
C)  $2,1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 2 } { 3 }$ 
D)  $- 2,1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 2 } { 3 }$ 
A)  $2 , - 1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 2 } { 3 }$ 
B)  $- 2 , - 1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , - \frac { 2 } { 3 }$ 
C)  $2,1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 2 } { 3 }$ 
D)  $- 2,1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 2 } { 3 }$

Question 10

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given.
-$a _ { 1 } = 19 ; \mathrm { d } = - 4$

Accepted Answer

A)  $23,18,13,8,3$ 
B)  $19,15,11,7,3$ 
C)  $0,19,15,11,7$ 
D)  $- 19 , - 15 , - 11 , - 7 , - 3$ 
A)  $23,18,13,8,3$ 
B)  $19,15,11,7,3$ 
C)  $0,19,15,11,7$ 
D)  $- 19 , - 15 , - 11 , - 7 , - 3$

Question 11

Use the partial sum formula to find the partial sum of the given geometric sequence.
-Find the sum of the first five terms of the geometric sequence $3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \ldots$

Accepted Answer

A)  $\frac { 3 } { 8 }$ 
B)  $\frac { 9 } { 16 }$ 
C)  93 
D)  $\frac { 93 } { 16 }$ 
A)  $\frac { 3 } { 8 }$ 
B)  $\frac { 9 } { 16 }$ 
C)  93 
D)  $\frac { 93 } { 16 }$

Question 12

Use Pascal's triangle to expand the binomial.
-$( m - n ) ^ { 5 }$

Accepted Answer

A)  $m ^ { 5 } - 5 m ^ { 4 } n - 10 m ^ { 3 } n ^ { 2 } - 10 m ^ { 2 } n ^ { 3 } - 5 m n ^ { 4 } - n ^ { 5 }$ 
B)  $m ^ { 5 } - n ^ { 5 }$ 
C)  $m ^ { 5 } - 6 m ^ { 4 } n + 15 m ^ { 3 } n ^ { 2 } - 20 m ^ { 3 } n ^ { 3 } + 15 m ^ { 2 } n ^ { 3 } - 6 m n ^ { 4 } + n ^ { 5 }$ 
D)  $m ^ { 5 } - 5 m ^ { 4 } n + 10 m ^ { 3 } n ^ { 2 } - 10 m ^ { 2 } n ^ { 3 } + 5 m n ^ { 4 } - n ^ { 5 }$ 
A)  $m ^ { 5 } - 5 m ^ { 4 } n - 10 m ^ { 3 } n ^ { 2 } - 10 m ^ { 2 } n ^ { 3 } - 5 m n ^ { 4 } - n ^ { 5 }$ 
B)  $m ^ { 5 } - n ^ { 5 }$ 
C)  $m ^ { 5 } - 6 m ^ { 4 } n + 15 m ^ { 3 } n ^ { 2 } - 20 m ^ { 3 } n ^ { 3 } + 15 m ^ { 2 } n ^ { 3 } - 6 m n ^ { 4 } + n ^ { 5 }$ 
D)  $m ^ { 5 } - 5 m ^ { 4 } n + 10 m ^ { 3 } n ^ { 2 } - 10 m ^ { 2 } n ^ { 3 } + 5 m n ^ { 4 } - n ^ { 5 }$

Question 13

Solve the problem.
-A pendulum swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only $\frac { 3 } { 5 }$ as far as on the previous swing. How far will it swing altogether before coming to a complete stop? If necessary, round to the nearest inch.

Accepted Answer

A)  $100 \mathrm { in }$. 
B)  $133 \mathrm { in }$. 
C)  $200 \mathrm { in }$. 
D)  $267 \mathrm { in }$. 
A)  $100 \mathrm { in }$. 
B)  $133 \mathrm { in }$. 
C)  $200 \mathrm { in }$. 
D)  $267 \mathrm { in }$.

Question 14

Solve the problem.
-The population of a small town is growing yearly according to the sequence defined by $a _ { n } = 450 + 55 ( n - 1 )$, where $n$ is the number of the year just beginning. Predict the population at the beginning of the eighth year. Find the town's initial population.

Accepted Answer

A)  890 people; 450 people initially 
B)  835 people; 505 people initially 
C)  835 people; 450 people initially 
D)  890 people; 505 people initially 
A)  890 people; 450 people initially 
B)  835 people; 505 people initially 
C)  835 people; 450 people initially 
D)  890 people; 505 people initially

Question 15

Find the indicated term of the sequence.
-The fifth term of the geometric sequence 4, -20, 100, ...

Accepted Answer

A)  -12,500 
B)  625 
C)  -2500 
D)  2500 
A)  -12,500 
B)  625 
C)  -2500 
D)  2500

Question 16

Find the indicated term.
-The fifth term of the expansion of $( 5 x + 4 ) ^ { 5 }$

Accepted Answer

A)  $6400 \mathrm { x }$ 
B)  5120 
C)  $8000 x ^ { 2 }$ 
D)  $1600 \mathrm { x }$ 
A)  $6400 \mathrm { x }$ 
B)  5120 
C)  $8000 x ^ { 2 }$ 
D)  $1600 \mathrm { x }$

Question 17

Find a general term an for the sequence whose first four terms are given.
-$8,24,40,56 , \ldots$

Accepted Answer

A)  $a _ { n } = 16 n - 2$ 
B)  $a _ { n } = 8 n - 16$ 
C)  $a _ { n } = 8 ( 16 ) ^ { n - 1 }$ 
D)  $a _ { n } = 4 ( 4 n - 2 )$ 
A)  $a _ { n } = 16 n - 2$ 
B)  $a _ { n } = 8 n - 16$ 
C)  $a _ { n } = 8 ( 16 ) ^ { n - 1 }$ 
D)  $a _ { n } = 4 ( 4 n - 2 )$

Question 18

Evaluate the expression.
-$\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } + 9 \right)$

Accepted Answer

A)  100 
B)  77 
C)  39 
D)  51 
A)  100 
B)  77 
C)  39 
D)  51

Question 19

Given are the first three terms of a sequence that is either arithmetic or geometric. If the sequence is arithmetic, find a1
and d. If a sequence is geometric, find a1 and r.
-$10,15,20 , \ldots$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 10 , \mathrm {~d} = 15$ 
B)  $a _ { 1 } = 10 , d = 5$ 
C)  $\mathrm { a } _ { 1 } = 10 , \mathrm {~d} = - 5$ 
D)  $a _ { 1 } = 10 , r = 5$ 
A)  $\mathrm { a } _ { 1 } = 10 , \mathrm {~d} = 15$ 
B)  $a _ { 1 } = 10 , d = 5$ 
C)  $\mathrm { a } _ { 1 } = 10 , \mathrm {~d} = - 5$ 
D)  $a _ { 1 } = 10 , r = 5$

Question 20

Find the sum of the terms of the infinite geometric sequence.
-$3 , - \frac { 3 } { 4 } , \frac { 3 } { 16 } , \cdots$

Accepted Answer

A)  $\frac { 9 } { 4 }$ 
B)  $- \frac { 3 } { 4 }$ 
C)  3 
D)  $\frac { 12 } { 5 }$ 
A)  $\frac { 9 } { 4 }$ 
B)  $- \frac { 3 } { 4 }$ 
C)  3 
D)  $\frac { 12 } { 5 }$

Find the indicated term(s) of the given sequence. -The first five terms of the sequence $a _ { n } = \frac { ( - 1 ) ^ { n } } { n ^ { 2 } - 3 }$

Find the indicated term of the sequence. -The ninth term of the arithmetic sequence $23,17,11 , \ldots$

Write the first five terms of the sequence whose general term is given. - $a _ { n } = ( - 2 ) ^ { n }$

Evaluate the expression. - $\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 5 i }$

Solve the problem. -The number of birds born each year at the local zoo forms a sequence whose general term is $a _ { n } = ( n + 9 ) ( n - 1 )$ . Find the number of birds born in the fourth year, and find the total number of birds born in the first four years.

Evaluate the expression. - $\sum _ { i = 2 } ^ { 4 } i ( i - 5 )$

Given are the first three terms of a sequence that is arithmetic. Find a1 and d. - $- 14 , - 17 , - 20$

Use the binomial formula to expand the binomial. - $( g - 2 h ) ^ { 3 }$

Write the first five terms of the sequence whose general term is given. - $a _ { n } = \frac { n + 1 } { 2 n - 1 }$

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given. - $a _ { 1 } = 19 ; \mathrm { d } = - 4$

Use the partial sum formula to find the partial sum of the given geometric sequence. -Find the sum of the first five terms of the geometric sequence $3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \ldots$

Use Pascal's triangle to expand the binomial. - $( m - n ) ^ { 5 }$

Solve the problem. -A pendulum swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only $\frac { 3 } { 5 }$ as far as on the previous swing. How far will it swing altogether before coming to a complete stop? If necessary, round to the nearest inch.

Solve the problem. -The population of a small town is growing yearly according to the sequence defined by $a _ { n } = 450 + 55 ( n - 1 )$ , where $n$ is the number of the year just beginning. Predict the population at the beginning of the eighth year. Find the town's initial population.

Find the indicated term of the sequence. -The fifth term of the geometric sequence 4, -20, 100, ...

Find the indicated term. -The fifth term of the expansion of $( 5 x + 4 ) ^ { 5 }$

Find a general term an for the sequence whose first four terms are given. - $8,24,40,56 , \ldots$

Evaluate the expression. - $\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } + 9 \right)$

Given are the first three terms of a sequence that is either arithmetic or geometric. If the sequence is arithmetic, find a1 and d. If a sequence is geometric, find a1 and r. - $10,15,20 , \ldots$

Find the sum of the terms of the infinite geometric sequence. - $3 , - \frac { 3 } { 4 } , \frac { 3 } { 16 } , \cdots$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Filters

Exam 14: Sequences, Series, and the Binomial Theorem

Find the indicated term(s) of the given sequence. -The first five terms of the sequence an=(−1)nn2−3a _ { n } = \frac { ( - 1 ) ^ { n } } { n ^ { 2 } - 3 }an​=n2−3(−1)n​

Find the indicated term of the sequence. -The ninth term of the arithmetic sequence 23,17,11,…23,17,11 , \ldots23,17,11,…

Write the first five terms of the sequence whose general term is given. - an=(−2)na _ { n } = ( - 2 ) ^ { n }an​=(−2)n

Evaluate the expression. - ∑i=1415i\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 5 i }∑i=14​5i1​

Solve the problem. -The number of birds born each year at the local zoo forms a sequence whose general term is an=(n+9)(n−1)a _ { n } = ( n + 9 ) ( n - 1 )an​=(n+9)(n−1) . Find the number of birds born in the fourth year, and find the total number of birds born in the first four years.

Evaluate the expression. - ∑i=24i(i−5)\sum _ { i = 2 } ^ { 4 } i ( i - 5 )∑i=24​i(i−5)

Given are the first three terms of a sequence that is arithmetic. Find a1 and d. - −14,−17,−20- 14 , - 17 , - 20−14,−17,−20

Use the binomial formula to expand the binomial. - (g−2h)3( g - 2 h ) ^ { 3 }(g−2h)3

Write the first five terms of the sequence whose general term is given. - an=n+12n−1a _ { n } = \frac { n + 1 } { 2 n - 1 }an​=2n−1n+1​

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given. - a1=19;d=−4a _ { 1 } = 19 ; \mathrm { d } = - 4a1​=19;d=−4

Use the partial sum formula to find the partial sum of the given geometric sequence. -Find the sum of the first five terms of the geometric sequence 3,32,34,…3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \ldots3,23​,43​,…

Use Pascal's triangle to expand the binomial. - (m−n)5( m - n ) ^ { 5 }(m−n)5

Solve the problem. -A pendulum swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only 35\frac { 3 } { 5 }53​ as far as on the previous swing. How far will it swing altogether before coming to a complete stop? If necessary, round to the nearest inch.