Question 1

Find the sum of the first n terms of the following arithmetic sequence.
-$a _ { 1 } = - 48 , d = - 31 ; n = 10$

Accepted Answer

A)  915 
B)  1635 
C)  -1635 
D)  -1875 
A)  915 
B)  1635 
C)  -1635 
D)  -1875

Question 2

Find a general term an for the geometric sequence.
-$$8 , - 2 , \frac { 1 } { 2 } , - \frac { 1 } { 8 } , \frac { 1 } { 32 } \ldots$$

Accepted Answer

A)  $a _ { n } = 8 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 6 \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = \frac { 1 } { 8 } ( - 4 ) ^{n - 1}$ 
D)  $a _ { n } = 8 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
A)  $a _ { n } = 8 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 6 \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = \frac { 1 } { 8 } ( - 4 ) ^{n - 1}$ 
D)  $a _ { n } = 8 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$

Question 3

Write out the first five terms of the sequence.
-$$a _ { n } = 2 ^ { n }$$

Accepted Answer

A)  $2,4,8,16,32$ 
B)  $1,2,4,8,16$ 
C)  $1,4,9,16,25$ 
D)  $4,8,16,32,64$ 
A)  $2,4,8,16,32$ 
B)  $1,2,4,8,16$ 
C)  $1,4,9,16,25$ 
D)  $4,8,16,32,64$

Question 4

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-

Accepted Answer

A)  $a _ { n } = n - 3$ 
B)  $a _ { n } = n + 4$ 
C)  $a _ { n } = n - 4$ 
D)  $a _ { n } = n + 3$ 
A)  $a _ { n } = n - 3$ 
B)  $a _ { n } = n + 4$ 
C)  $a _ { n } = n - 4$ 
D)  $a _ { n } = n + 3$

Question 5

Find the sum of the first n terms of the following arithmetic sequence.
-Find the sum of the first 293 positive odd integers.

Accepted Answer

A)  86,142 
B)  85,849 
C)  86,436 
D)  85,264 
A)  86,142 
B)  85,849 
C)  86,436 
D)  85,264

Question 6

Write the series using summation notation.
-$$\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 5 } \frac { i } { i ( i + 1 ) }$ 
B)  $\sum _ { i = 1 } ^ { 5 } \frac { i + 2 } { i ( i - 1 ) }$ 
C)  $\sum _ { i = 1 } ^ { 5 } \frac { i + 2 } { i ( i + 1 ) }$ 
D)  $\sum _ { i = 1 } ^ { 5 } \frac { i - 2 } { i ( i + 1 ) }$ 
A)  $\sum _ { i = 1 } ^ { 5 } \frac { i } { i ( i + 1 ) }$ 
B)  $\sum _ { i = 1 } ^ { 5 } \frac { i + 2 } { i ( i - 1 ) }$ 
C)  $\sum _ { i = 1 } ^ { 5 } \frac { i + 2 } { i ( i + 1 ) }$ 
D)  $\sum _ { i = 1 } ^ { 5 } \frac { i - 2 } { i ( i + 1 ) }$

Question 7

Evaluate the expression.
-P(9, 9)

Accepted Answer

A)  9 
B)  181,440 
C)  362,880 
D)  1 
A)  9 
B)  181,440 
C)  362,880 
D)  1

Question 8

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = - 16 , a _ { 5 } = 128$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 8 , \mathrm { r } = - 2$ 
B)  $\mathrm { a } _ { 1 } = 8 , \mathrm { r } = - 0.5$ 
C)  a $\mathrm { a } _ { 1 } = 128 , \mathrm { r } = - 0.5$ 
D)  $\mathrm { a } _ { 1 } = 16 , \mathrm { r } = 2$ 
A)  $\mathrm { a } _ { 1 } = 8 , \mathrm { r } = - 2$ 
B)  $\mathrm { a } _ { 1 } = 8 , \mathrm { r } = - 0.5$ 
C)  a $\mathrm { a } _ { 1 } = 128 , \mathrm { r } = - 0.5$ 
D)  $\mathrm { a } _ { 1 } = 16 , \mathrm { r } = 2$

Question 9

Decide whether the given sequence is finite or infinite.
-6, 7, 8, 9

Accepted Answer

A)  Infinite 
B)  Finite 
A)  Infinite 
B)  Finite

Question 10

Write the binomial expansion of the expression.
-$( 2 m - 4 n ) ^ { 4 }$

Accepted Answer

A)  $16 m ^ { 4 } - 128 m ^ { 3 } n + 384 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } + 256 n ^ { 4 }$ 
B)  $16 m ^ { 4 } - 2048 m ^ { 3 } n + 2304 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } + 256 n ^ { 4 }$ 
C)  $16 m ^ { 4 } - 2048 m ^ { 3 } n - 2304 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } - 256 n ^ { 4 }$ 
D)  $16 m ^ { 4 } - 128 m ^ { 3 } n - 384 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } - 256 n ^ { 4 }$ 
A)  $16 m ^ { 4 } - 128 m ^ { 3 } n + 384 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } + 256 n ^ { 4 }$ 
B)  $16 m ^ { 4 } - 2048 m ^ { 3 } n + 2304 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } + 256 n ^ { 4 }$ 
C)  $16 m ^ { 4 } - 2048 m ^ { 3 } n - 2304 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } - 256 n ^ { 4 }$ 
D)  $16 m ^ { 4 } - 128 m ^ { 3 } n - 384 m ^ { 2 } n ^ { 2 } - 512 m n ^ { 3 } - 256 n ^ { 4 }$

Question 11

Find the sum of the first n terms of the following arithmetic sequence.
-$a _ { 1 } = - 7 , d = 2 ; n = 5$

Accepted Answer

A)  -35 
B)  -15 
C)  3 
D)  -10 
A)  -35 
B)  -15 
C)  3 
D)  -10

Question 12

Use a calculator to evaluate the expression.
-${ } _ { 16 } C _ { 8 }$

Accepted Answer

A)  12,870 
B)  64,864,800 
C)  5.189 × 108 
D)  25,740 
A)  12,870 
B)  64,864,800 
C)  5.189 × 108 
D)  25,740

Question 13

Evaluate the sum using the given information.
-$$\begin{array} { l } 
x _ { 1 } = 2 , x _ { 2 } = 4 , x _ { 3 } = 5 , x _ { 4 } = 0 \text {, and } \Delta x = - 0.3 ; f ( x ) = 3 x ^ { 2 } - x \
\sum _ { i = 1 } ^ { 4 } f \left( x _ { i } \right) \Delta x
\end{array}$$

Accepted Answer

A)  5.193 
B)  -148.8 
C)  -37.2 
D)  -36.2 
A)  5.193 
B)  -148.8 
C)  -37.2 
D)  -36.2

Question 14

Evaluate the sum using the given information.
-$$\mathrm { x } _ { 1 } = 5 , \mathrm { x } _ { 2 } = 4 , \mathrm { x } _ { 3 } = - 5 , \mathrm { x } _ { 4 } = 3 \text {, and } \Delta \mathrm { x } = - 0.3 ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 }$$
$$\sum _ { \mathrm { i } = 1 } ^ { 4 } \mathrm { f } \left( \mathrm { x } _ { \mathrm { i } } \right) \Delta \mathrm { x }$$

Accepted Answer

A)  $- 0.6795$ 
B)  $- 90$ 
C)  $- 17.1$ 
D)  $- 22.5$ 
A)  $- 0.6795$ 
B)  $- 90$ 
C)  $- 17.1$ 
D)  $- 22.5$

Question 15

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } .$$
-$$\sum _ { i = 1 } ^ { 6 } \left( i ^ { 2 } + i - 4 \right)$$

Accepted Answer

A)  417 
B)  108 
C)  88 
D)  437 
A)  417 
B)  108 
C)  88 
D)  437

Question 16

Find the common ratio r for the given infinite geometric sequence.
-$$75,30,12,4.8,1.92 , \ldots$$

Accepted Answer

A)  $2.5$ 
B)  $- 0.4$ 
C)  $1.92$ 
D)  $0.4$ 
A)  $2.5$ 
B)  $- 0.4$ 
C)  $1.92$ 
D)  $0.4$

Question 17

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } .$$
-$$\sum _ { i = 1 } ^ { 6 } ( 3 i - 2 )$$

Accepted Answer

A)  57 
B)  39 
C)  63 
D)  51 
A)  57 
B)  39 
C)  63 
D)  51

Question 18

Write the indicated term of the binomial expansion.
-$( 5 x + 3 ) ^ { 5 } ; 5$ th term

Accepted Answer

A)  $3375 x ^ { 2 }$ 
B)  1215 
C)  $2025 x$ 
D)  $675 \mathrm { x }$ 
A)  $3375 x ^ { 2 }$ 
B)  1215 
C)  $2025 x$ 
D)  $675 \mathrm { x }$

Question 19

Provide an appropriate response.
-Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

Accepted Answer

A)  Permutation 
B)  Neither 
C)  Combination 
A)  Permutation 
B)  Neither 
C)  Combination

Question 20

Find the sum of the first n terms of the following arithmetic sequence.
-Find the sum of the first 986 positive integers.

Accepted Answer

A)  972,196 
B)  486591 
C)  485605 
D)  973,182 
A)  972,196 
B)  486591 
C)  485605 
D)  973,182

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 1 } = - 48 , d = - 31 ; n = 10$

Find a general term an for the geometric sequence. - $8 , - 2 , \frac { 1 } { 2 } , - \frac { 1 } { 8 } , \frac { 1 } { 32 } \ldots$

Write out the first five terms of the sequence. - $a _ { n } = 2 ^ { n }$

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

Find the sum of the first n terms of the following arithmetic sequence. -Find the sum of the first 293 positive odd integers.

Write the series using summation notation. - $\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }$

Evaluate the expression. -P(9, 9)

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = - 16 , a _ { 5 } = 128$

Decide whether the given sequence is finite or infinite. -6, 7, 8, 9

Write the binomial expansion of the expression. - $( 2 m - 4 n ) ^ { 4 }$

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 1 } = - 7 , d = 2 ; n = 5$

Use a calculator to evaluate the expression. - ${ } _ { 16 } C _ { 8 }$

Evaluate the sum using the given information. - =2,=4,=5,=0 , and \Deltax=-0.3;f(x)=3-x f \Deltax

Find the common ratio r for the given infinite geometric sequence. - $75,30,12,4.8,1.92 , \ldots$

Write the indicated term of the binomial expansion. - $( 5 x + 3 ) ^ { 5 } ; 5$ th term

Provide an appropriate response. -Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

Find the sum of the first n terms of the following arithmetic sequence. -Find the sum of the first 986 positive integers.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Filters

Exam 12: Further Topics in Algebra

Find the sum of the first n terms of the following arithmetic sequence. - a1=−48,d=−31;n=10a _ { 1 } = - 48 , d = - 31 ; n = 10a1​=−48,d=−31;n=10

Find a general term an for the geometric sequence. - 8,−2,12,−18,132…8 , - 2 , \frac { 1 } { 2 } , - \frac { 1 } { 8 } , \frac { 1 } { 32 } \ldots8,−2,21​,−81​,321​…

Write out the first five terms of the sequence. - an=2na _ { n } = 2 ^ { n }an​=2n