Question 1

Write out the first five terms of the sequence.
-$a_{n}=(-1)^{n-7}$

Accepted Answer

A)  $-1,1,-1,1,-1$ 
B)  $-1,-1,-1,-1,-1$ 
C)  $1,-1,1,-1,1$ 
D)  1, 1, 1, 1, 1 
A)  $-1,1,-1,1,-1$ 
B)  $-1,-1,-1,-1,-1$ 
C)  $1,-1,1,-1,1$ 
D)  1, 1, 1, 1, 1

Question 2

10 !

Accepted Answer

A)  $121,645,100,408,832,000$ 
B)  362,880 
C)  $39,916,800$ 
D)  $3,628,800$ 
A)  $121,645,100,408,832,000$ 
B)  362,880 
C)  $39,916,800$ 
D)  $3,628,800$

Question 3

Evaluate the series
-$\sum_{\mathrm{i}=3}^{6} \frac{\left(\mathrm{i}^{2}-2\right)}{2}$

Accepted Answer

A)  39 
B)  40 
C)  78 
D)  21 
A)  39 
B)  40 
C)  78 
D)  21

Question 4

Evaluate the expression
-$2 ! \cdot 5$

Accepted Answer

A)  240 
B)  $3,628,800$ 
C)  7 
D)  10 
A)  240 
B)  $3,628,800$ 
C)  7 
D)  10

Question 5

Find a general term, $a_{n}$, for the given terms of the sequence.
-$1,4,7,10,13, \ldots$

Accepted Answer

A)  $a_{n}=3^{n-1}$ 
B)  $a_{n}=2 n-3$ 
C)  $a_{n}=n+3$ 
D)  $a_{n}=3 n-2$ 
A)  $a_{n}=3^{n-1}$ 
B)  $a_{n}=2 n-3$ 
C)  $a_{n}=n+3$ 
D)  $a_{n}=3 n-2$

Question 6

Find the sum if it exists.
-$\sum_{i=1}^{6}(6 i-3)$

Accepted Answer

A)  108 
B)  1165 
C)  76 
D)  75 
A)  108 
B)  1165 
C)  76 
D)  75

Question 7

Write the first four terms of the binomial expansion.
-$(m+3 n)^{13}$

Accepted Answer

A)  $m^{13}+3 m^{12} n+9 m^{11} n^{2}+27 m^{10} n^{3}$ 
B)  $m^{13}+39 m^{12} n+702 m^{11} n^{2}+7722 m^{10} n^{3}$ 
C)  $m^{13}+39 m^{12} n+234 m^{11} n^{2}+858 m^{10} n^{3}$ 
D)  $m^{13}+13 m^{12} n+78 m^{11} n^{2}+286 m^{10} n^{3}$ 
A)  $m^{13}+3 m^{12} n+9 m^{11} n^{2}+27 m^{10} n^{3}$ 
B)  $m^{13}+39 m^{12} n+702 m^{11} n^{2}+7722 m^{10} n^{3}$ 
C)  $m^{13}+39 m^{12} n+234 m^{11} n^{2}+858 m^{10} n^{3}$ 
D)  $m^{13}+13 m^{12} n+78 m^{11} n^{2}+286 m^{10} n^{3}$

Question 8

Write out the terms of the series.
-$\sum_{i=1}^{4}(x+i)$

Accepted Answer

A)  $(x+1)+(x+2)+(x+3)$ 
B)  $(x+2)+(x+3)+(x+4)+(x+5)$ 
C)  $x+(x+1)+(x+2)+(x+3)$ 
D)  $(x+1)+(x+2)+(x+3)+(x+4)$ 
A)  $(x+1)+(x+2)+(x+3)$ 
B)  $(x+2)+(x+3)+(x+4)+(x+5)$ 
C)  $x+(x+1)+(x+2)+(x+3)$ 
D)  $(x+1)+(x+2)+(x+3)+(x+4)$

Question 9

The number of mutual funds available to investors in Dereguland for each year period the period $1996-2000$ is given in the following table.
 
To the nearest whole number, what was the average number of funds available during this period?

Accepted Answer

A)  12,461 
B)  5070 
C)  4984 
D)  4910 
A)  12,461 
B)  5070 
C)  4984 
D)  4910

Question 10

A town has a population of 10,000 people and is increasing by $10 \%$ every year. What will the population be at the end of 4 years?

Accepted Answer

A)  13,310 people 
B)  14,000 people 
C)  4641 people 
D)  14,641 people 
A)  13,310 people 
B)  14,000 people 
C)  4641 people 
D)  14,641 people

Question 11

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence.
-$a_{1}=-4, d=\frac{5}{3}$

Accepted Answer

A)  $a_{n}=\frac{5}{3}+\frac{7}{3} n$ 
B)  $a_{n}=\frac{5}{3} n-\frac{17}{3}$ 
C)  $a_{n}=\frac{5}{3} n-\frac{7}{3}$ 
D)  $a_{n}=4 n-\frac{7}{3}$ 
A)  $a_{n}=\frac{5}{3}+\frac{7}{3} n$ 
B)  $a_{n}=\frac{5}{3} n-\frac{17}{3}$ 
C)  $a_{n}=\frac{5}{3} n-\frac{7}{3}$ 
D)  $a_{n}=4 n-\frac{7}{3}$

Question 12

Give an example of a geometric sequence with $\mathrm{a}_{4}=54$.

Accepted Answer

Examples will vary.

Question 13

Find the arithmetic mean for the collection of numbers.
$7,13,3,15,12$

Accepted Answer

A)  51 
B)  10 
C)  9 
D)  12.5 
A)  51 
B)  10 
C)  9 
D)  12.5

Question 14

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence.
-$1,-3,9,-27,81$

Accepted Answer

A)  121 
B)  -121 
C)  -61 
D)  61 
A)  121 
B)  -121 
C)  -61 
D)  61

Question 15

Write the first five terms of the arithmetic sequence.
-$\mathrm{a}_{1}=-5, \mathrm{~d}=-2$

Accepted Answer

A)  $5,7,9,11,13$ 
B)  $7,9,11,13,15$ 
C)  $-7,-9,-11,-13,-15$ 
D)  $-5,-7,-9,-11,-13$ 
A)  $5,7,9,11,13$ 
B)  $7,9,11,13,15$ 
C)  $-7,-9,-11,-13,-15$ 
D)  $-5,-7,-9,-11,-13$

Question 16

Find the indicated term of the binomial expansion.
-$(3 x+4)^{5}$; 5th term

Accepted Answer

A)  $2880 x^{2}$ 
B)  $3840 x$ 
C)  $960 x$ 
D)  5120 
A)  $2880 x^{2}$ 
B)  $3840 x$ 
C)  $960 x$ 
D)  5120

Question 17

Find the indicated term for the geometric sequence.
-$\mathrm{a}_{1}=10, \mathrm{r}=\frac{1}{3} ; \mathrm{a}_{7}$

Accepted Answer

A)  $\frac{10}{243}$ 
B)  $\frac{10}{2187}$ 
C)  $\frac{10}{729}$ 
D)  $\frac{1}{243}$ 
A)  $\frac{10}{243}$ 
B)  $\frac{10}{2187}$ 
C)  $\frac{10}{729}$ 
D)  $\frac{1}{243}$

Question 18

Find the arithmetic mean for the collection of numbers.
$1,13,-3,4,15$

Accepted Answer

A)  13 
B)  7.5 
C)  4 
D)  6 
A)  13 
B)  7.5 
C)  4 
D)  6

Question 19

Write out the terms of the series.
-$\sum_{i=1}^{5} i \cdot x^{i}$

Accepted Answer

A)  $x+x^{2}+x^{3}+x^{4}+x^{5}$ 
B)  $x+2 x^{2}+3 x^{3}+4 x^{4}+5 x^{5}+\ldots$ 
C)  $1+2 x^{2}+3 x^{3}+4 x^{4}+5 x^{5}$ 
D)  $x+2 x^{2}+3 x^{3}+4 x^{4}+5 x^{5}$ 
A)  $x+x^{2}+x^{3}+x^{4}+x^{5}$ 
B)  $x+2 x^{2}+3 x^{3}+4 x^{4}+5 x^{5}+\ldots$ 
C)  $1+2 x^{2}+3 x^{3}+4 x^{4}+5 x^{5}$ 
D)  $x+2 x^{2}+3 x^{3}+4 x^{4}+5 x^{5}$

Question 20

Find the number of terms in the arithmetic sequence.
-$9,17,25, \ldots, 105$

Accepted Answer

A)  13 
B)  14 
C)  11 
D)  12 
A)  13 
B)  14 
C)  11 
D)  12

Write out the first five terms of the sequence. - $a_{n}=(-1)^{n-7}$

10 !

Evaluate the series - $\sum_{\mathrm{i}=3}^{6} \frac{\left(\mathrm{i}^{2}-2\right)}{2}$

Evaluate the expression - $2 ! \cdot 5$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $1,4,7,10,13, \ldots$

Find the sum if it exists. - $\sum_{i=1}^{6}(6 i-3)$

Write the first four terms of the binomial expansion. - $(m+3 n)^{13}$

Write out the terms of the series. - $\sum_{i=1}^{4}(x+i)$

The number of mutual funds available to investors in Dereguland for each year period the period $1996-2000$ is given in the following table. To the nearest whole number, what was the average number of funds available during this period?

A town has a population of 10,000 people and is increasing by $10 \%$ every year. What will the population be at the end of 4 years?

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence. - $a_{1}=-4, d=\frac{5}{3}$

Give an example of a geometric sequence with $\mathrm{a}_{4}=54$ .

Find the arithmetic mean for the collection of numbers. $7,13,3,15,12$

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence. - $1,-3,9,-27,81$

Write the first five terms of the arithmetic sequence. - $\mathrm{a}_{1}=-5, \mathrm{~d}=-2$

Find the indicated term of the binomial expansion. - $(3 x+4)^{5}$ ; 5th term

Find the indicated term for the geometric sequence. - $\mathrm{a}_{1}=10, \mathrm{r}=\frac{1}{3} ; \mathrm{a}_{7}$

Find the arithmetic mean for the collection of numbers. $1,13,-3,4,15$

Write out the terms of the series. - $\sum_{i=1}^{5} i \cdot x^{i}$

Find the number of terms in the arithmetic sequence. - $9,17,25, \ldots, 105$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Appendices

Filters

Exam 12: Further Topics in Algebra

Write out the first five terms of the sequence. - an=(−1)n−7a_{n}=(-1)^{n-7}an​=(−1)n−7

10 !

Evaluate the series - ∑i=36(i2−2)2\sum_{\mathrm{i}=3}^{6} \frac{\left(\mathrm{i}^{2}-2\right)}{2}∑i=36​2(i2−2)​

Evaluate the expression - 2!⋅52 ! \cdot 52!⋅5

Find a general term, ana_{n}an​ , for the given terms of the sequence. - 1,4,7,10,13,…1,4,7,10,13, \ldots1,4,7,10,13,…

Find the sum if it exists. - ∑i=16(6i−3)\sum_{i=1}^{6}(6 i-3)∑i=16​(6i−3)

Write the first four terms of the binomial expansion. - (m+3n)13(m+3 n)^{13}(m+3n)13

Write out the terms of the series. - ∑i=14(x+i)\sum_{i=1}^{4}(x+i)∑i=14​(x+i)

The number of mutual funds available to investors in Dereguland for each year period the period 1996−20001996-20001996−2000 is given in the following table. To the nearest whole number, what was the average number of funds available during this period?

A town has a population of 10,000 people and is increasing by 10%10 \%10% every year. What will the population be at the end of 4 years?

Use the formula for ana_{n}an​ to find the general term for the arithmetic sequence. - a1=−4,d=53a_{1}=-4, d=\frac{5}{3}a1​=−4,d=35​

Give an example of a geometric sequence with a4=54\mathrm{a}_{4}=54a4​=54 .

Find the arithmetic mean for the collection of numbers. 7,13,3,15,127,13,3,15,127,13,3,15,12

Use the formula for Sn\mathbf{S}_{\mathbf{n}}Sn​ to find the sum for the geometric sequence. - 1,−3,9,−27,811,-3,9,-27,811,−3,9,−27,81

Write the first five terms of the arithmetic sequence. - a1=−5, d=−2\mathrm{a}_{1}=-5, \mathrm{~d}=-2a1​=−5, d=−2

Find the indicated term of the binomial expansion. - (3x+4)5(3 x+4)^{5}(3x+4)5 ; 5th term

Find the indicated term for the geometric sequence. - a1=10,r=13;a7\mathrm{a}_{1}=10, \mathrm{r}=\frac{1}{3} ; \mathrm{a}_{7}a1​=10,r=31​;a7​

Find the arithmetic mean for the collection of numbers. 1,13,−3,4,151,13,-3,4,151,13,−3,4,15

Write out the terms of the series. - ∑i=15i⋅xi\sum_{i=1}^{5} i \cdot x^{i}∑i=15​i⋅xi

Find the number of terms in the arithmetic sequence. - 9,17,25,…,1059,17,25, \ldots, 1059,17,25,…,105

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Appendices

Filters

Write out the first five terms of the sequence. - $a_{n}=(-1)^{n-7}$

Evaluate the series - $\sum_{\mathrm{i}=3}^{6} \frac{\left(\mathrm{i}^{2}-2\right)}{2}$

Evaluate the expression - $2 ! \cdot 5$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $1,4,7,10,13, \ldots$

Find the sum if it exists. - $\sum_{i=1}^{6}(6 i-3)$

Write the first four terms of the binomial expansion. - $(m+3 n)^{13}$

Write out the terms of the series. - $\sum_{i=1}^{4}(x+i)$

The number of mutual funds available to investors in Dereguland for each year period the period $1996-2000$ is given in the following table. To the nearest whole number, what was the average number of funds available during this period?

A town has a population of 10,000 people and is increasing by $10 \%$ every year. What will the population be at the end of 4 years?

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence. - $a_{1}=-4, d=\frac{5}{3}$

Give an example of a geometric sequence with $\mathrm{a}_{4}=54$ .

Find the arithmetic mean for the collection of numbers. $7,13,3,15,12$

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence. - $1,-3,9,-27,81$

Write the first five terms of the arithmetic sequence. - $\mathrm{a}_{1}=-5, \mathrm{~d}=-2$

Find the indicated term of the binomial expansion. - $(3 x+4)^{5}$ ; 5th term

Find the indicated term for the geometric sequence. - $\mathrm{a}_{1}=10, \mathrm{r}=\frac{1}{3} ; \mathrm{a}_{7}$

Find the arithmetic mean for the collection of numbers. $1,13,-3,4,15$

Write out the terms of the series. - $\sum_{i=1}^{5} i \cdot x^{i}$

Find the number of terms in the arithmetic sequence. - $9,17,25, \ldots, 105$