Question 1

Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\mathrm{a}_{1}=7, \mathrm{r}=\frac{1}{5}$

Accepted Answer

A)  $\frac{35}{6}$ 
B)  $\frac{7}{6}$ 
C)  $\frac{7}{4}$ 
D)  $\frac{35}{4}$ 
A)  $\frac{35}{6}$ 
B)  $\frac{7}{6}$ 
C)  $\frac{7}{4}$ 
D)  $\frac{35}{4}$

Question 2

Use the binomial theorem to expand the expression.
-$(a-b)^{6}$

Accepted Answer

A)  $a^{6}+6 a^{5} b+15 a^{4} b^{2}+20 a^{3} b^{3}+15 a^{2} b^{4}+6 a b^{5}+b^{6}$ 
B)  $a^{6}-6 a^{5} b-15 a^{4} b^{2}-20 a^{3} b^{3}-15 a^{2} b^{4}-6 a b^{5}-b^{6}$ 
C)  $-a^{6}+6 a^{5} b-15 a^{4} b^{2}+20 a^{3} b^{3}-15 a^{2} b^{4}+6 a b^{5}-b^{6}$ 
D)  $a^{6}-6 a^{5} b+15 a^{4} b^{2}-20 a^{3} b^{3}+15 a^{2} b^{4}-6 a b^{5}+b^{6}$ 
A)  $a^{6}+6 a^{5} b+15 a^{4} b^{2}+20 a^{3} b^{3}+15 a^{2} b^{4}+6 a b^{5}+b^{6}$ 
B)  $a^{6}-6 a^{5} b-15 a^{4} b^{2}-20 a^{3} b^{3}-15 a^{2} b^{4}-6 a b^{5}-b^{6}$ 
C)  $-a^{6}+6 a^{5} b-15 a^{4} b^{2}+20 a^{3} b^{3}-15 a^{2} b^{4}+6 a b^{5}-b^{6}$ 
D)  $a^{6}-6 a^{5} b+15 a^{4} b^{2}-20 a^{3} b^{3}+15 a^{2} b^{4}-6 a b^{5}+b^{6}$

Question 3

Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\mathrm{a}_{1}=5, \mathrm{r}=-\frac{1}{3}$

Accepted Answer

A)  $\frac{15}{4}$ 
B)  $\frac{10}{3}$ 
C)  $\frac{15}{2}$ 
D)  Does not exist 
A)  $\frac{15}{4}$ 
B)  $\frac{10}{3}$ 
C)  $\frac{15}{2}$ 
D)  Does not exist

Question 4

Find the indicated term for the sequence.
-$\mathrm{a}_{\mathrm{n}}=\frac{2 \mathrm{n}-1}{3 \mathrm{n}+4} ; \mathrm{a}_{13}$

Accepted Answer

A)  $\frac{25}{43}$ 
B)  $\frac{23}{43}$ 
C)  $\frac{5}{8}$ 
D)  $\frac{23}{40}$ 
A)  $\frac{25}{43}$ 
B)  $\frac{23}{43}$ 
C)  $\frac{5}{8}$ 
D)  $\frac{23}{40}$

Question 5

Find a general term, $a_{n}$, for the given terms of the sequence.
-$0,2,6,12,20, \ldots$

Accepted Answer

A)  $a_{n}=2^{n-1}-1$ 
B)  $a_{n}=2 n-2$ 
C)  $a_{n}=4 n-6$ 
D)  $a_{n}=n^{2}-n$ 
A)  $a_{n}=2^{n-1}-1$ 
B)  $a_{n}=2 n-2$ 
C)  $a_{n}=4 n-6$ 
D)  $a_{n}=n^{2}-n$

Question 6

The number of mutual funds available to investors in Dereguland for each year during 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)  5102 
B)  5099 
C)  12,393 
D)  4957 
A)  5102 
B)  5099 
C)  12,393 
D)  4957

Question 7

Suppose you invest $\$ 8900$ at the end of each year into an account earning $6 \%$ interest (compounded annually). At the end of 6 years, how much money will be in the account?

Accepted Answer

A)  $\$ 62,080.30$ 
B)  $\$ 61,835.30$ 
C)  $\$ 210,413.70$ 
D)  $\$ 60,857.80$ 
A)  $\$ 62,080.30$ 
B)  $\$ 61,835.30$ 
C)  $\$ 210,413.70$ 
D)  $\$ 60,857.80$

Question 8

$\frac{9 !}{6 ! 3 !}$

Accepted Answer

A)  84 
B)  362,880 
C)  60,480 
D)  504 
A)  84 
B)  362,880 
C)  60,480 
D)  504

Question 9

Why is it not possible to have a sequence with alternating signs that is an arithmetic sequence?

Accepted Answer

Answers may vary. One possibility: If th

Question 10

Use a formula for $S_{\mathbf{n}}$ to evaluate the series.
-$\sum_{i=1}^{7532} i$

Accepted Answer

A)  7533 
B)  $28,361,746$ 
C)  $28,369,278$ 
D)  7531 
A)  7533 
B)  $28,361,746$ 
C)  $28,369,278$ 
D)  7531

Question 11

Find the sum if it exists.
-$\sum_{\mathrm{i}=1}^{\infty}\left(\frac{4}{9}\right)^{\mathrm{i}}$

Accepted Answer

A)  $\frac{5}{4}$ 
B)  $\frac{4}{5}$ 
C)  $-\frac{4}{5}$ 
D)  Does not exist 
A)  $\frac{5}{4}$ 
B)  $\frac{4}{5}$ 
C)  $-\frac{4}{5}$ 
D)  Does not exist

Question 12

Find a general term, $a_{n}$, for the given terms of the sequence.
-$6,14,22,30,38, \ldots$

Accepted Answer

A)  $a_{n}=8 n-1$ 
B)  $a_{n}=2 n-8$ 
C)  $a_{n}=2(4 n-1)$ 
D)  $a_{n}=6(8)^{n-1}$ 
A)  $a_{n}=8 n-1$ 
B)  $a_{n}=2 n-8$ 
C)  $a_{n}=2(4 n-1)$ 
D)  $a_{n}=6(8)^{n-1}$

Question 13

Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\left.\sum_{i=1}^{\infty}(-9),\left(-\frac{9}{7}\right)\right)^{i}$

Accepted Answer

A)  $-\frac{162}{49}$ 
B)  $\frac{9}{7}$ 
C)  $\frac{1296}{49}$ 
D)  Does not exist 
A)  $-\frac{162}{49}$ 
B)  $\frac{9}{7}$ 
C)  $\frac{1296}{49}$ 
D)  Does not exist

Question 14

Find the indicated term of the binomial expansion.
-$(4 x-3 y)^{11} ; 10$ th term

Accepted Answer

A)  $-17,321,040 x^{2} y^{9}$ 
B)  $-4,330,260 x^{9} y^{2}$ 
C)  $5,773,680 x^{2} y^{10}$ 
D)  $5,773,680 x^{9} y^{2}$ 
A)  $-17,321,040 x^{2} y^{9}$ 
B)  $-4,330,260 x^{9} y^{2}$ 
C)  $5,773,680 x^{2} y^{10}$ 
D)  $5,773,680 x^{9} y^{2}$

Question 15

In your own words, explain how to determine the binomial coefficient for $x^{5} y^{4}$ in the expansion of $(x+y)^{9}$.

Accepted Answer

The numerator of the binomial coefficien

Question 16

Find $a_{4}$ for the sequence described.
-Arithmetic, with $a_{1}=7$ and $d=-5$

Accepted Answer

A)  -3 
B)  22 
C)  -8 
D)  2 
A)  -3 
B)  22 
C)  -8 
D)  2

Question 17

Find the indicated term for the geometric sequence.
-$\mathrm{a}_{1}=6, \mathrm{r}=-2$; $\mathrm{a}_{14}$

Accepted Answer

A)  -8192 
B)  $-49,152$ 
C)  8192 
D)  49,152 
A)  -8192 
B)  $-49,152$ 
C)  8192 
D)  49,152

Question 18

Evaluate the series
-$\sum_{i=1}^{4}\left(i^{2}-4 i-3\right)$

Accepted Answer

A)  -22 
B)  -2 
C)  -18 
D)  23 
A)  -22 
B)  -2 
C)  -18 
D)  23

Question 19

Find the requested sum for the arithmetic sequence.
-$a_{n}=-3 n-9 ; S_{5}$

Accepted Answer

A)  -60 
B)  0 
C)  -90 
D)  -24 
A)  -60 
B)  0 
C)  -90 
D)  -24

Question 20

Write the first five terms of the sequence described
-Arithmetic, with $a_{1}=23, d=7$

Accepted Answer

A)  $23,7,37,44,51$ 
B)  $7,30,53,76,99$ 
C)  $23,30,37,44,51$ 
D)  $23,7,60,90,120$ 
A)  $23,7,37,44,51$ 
B)  $7,30,53,76,99$ 
C)  $23,30,37,44,51$ 
D)  $23,7,60,90,120$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\mathrm{a}_{1}=7, \mathrm{r}=\frac{1}{5}$

Use the binomial theorem to expand the expression. - $(a-b)^{6}$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\mathrm{a}_{1}=5, \mathrm{r}=-\frac{1}{3}$

Find the indicated term for the sequence. - $\mathrm{a}_{\mathrm{n}}=\frac{2 \mathrm{n}-1}{3 \mathrm{n}+4} ; \mathrm{a}_{13}$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $0,2,6,12,20, \ldots$

The number of mutual funds available to investors in Dereguland for each year during 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?

Suppose you invest $\$ 8900$ at the end of each year into an account earning $6 \%$ interest (compounded annually). At the end of 6 years, how much money will be in the account?

$\frac{9 !}{6 ! 3 !}$

Why is it not possible to have a sequence with alternating signs that is an arithmetic sequence?

Use a formula for $S_{\mathbf{n}}$ to evaluate the series. - $\sum_{i=1}^{7532} i$

Find the sum if it exists. - $\sum_{\mathrm{i}=1}^{\infty}\left(\frac{4}{9}\right)^{\mathrm{i}}$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $6,14,22,30,38, \ldots$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\left.\sum_{i=1}^{\infty}(-9),\left(-\frac{9}{7}\right)\right)^{i}$

Find the indicated term of the binomial expansion. - $(4 x-3 y)^{11} ; 10$ th term

In your own words, explain how to determine the binomial coefficient for $x^{5} y^{4}$ in the expansion of $(x+y)^{9}$ .

Find $a_{4}$ for the sequence described. -Arithmetic, with $a_{1}=7$ and $d=-5$

Find the indicated term for the geometric sequence. - $\mathrm{a}_{1}=6, \mathrm{r}=-2$ ; $\mathrm{a}_{14}$

Evaluate the series - $\sum_{i=1}^{4}\left(i^{2}-4 i-3\right)$

Find the requested sum for the arithmetic sequence. - $a_{n}=-3 n-9 ; S_{5}$

Write the first five terms of the sequence described -Arithmetic, with $a_{1}=23, d=7$

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

Find the sum, if it exists, of the terms of the infinite geometric sequence. - a1=7,r=15\mathrm{a}_{1}=7, \mathrm{r}=\frac{1}{5}a1​=7,r=51​

Use the binomial theorem to expand the expression. - (a−b)6(a-b)^{6}(a−b)6

Find the sum, if it exists, of the terms of the infinite geometric sequence. - a1=5,r=−13\mathrm{a}_{1}=5, \mathrm{r}=-\frac{1}{3}a1​=5,r=−31​

Find the indicated term for the sequence. - an=2n−13n+4;a13\mathrm{a}_{\mathrm{n}}=\frac{2 \mathrm{n}-1}{3 \mathrm{n}+4} ; \mathrm{a}_{13}an​=3n+42n−1​;a13​

Find a general term, ana_{n}an​ , for the given terms of the sequence. - 0,2,6,12,20,…0,2,6,12,20, \ldots0,2,6,12,20,…

The number of mutual funds available to investors in Dereguland for each year during 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?

Suppose you invest $8900\$ 8900$8900 at the end of each year into an account earning 6%6 \%6% interest (compounded annually). At the end of 6 years, how much money will be in the account?

9!6!3!\frac{9 !}{6 ! 3 !}6!3!9!​

Why is it not possible to have a sequence with alternating signs that is an arithmetic sequence?

Use a formula for SnS_{\mathbf{n}}Sn​ to evaluate the series. - ∑i=17532i\sum_{i=1}^{7532} i∑i=17532​i

Find the sum if it exists. - ∑i=1∞(49)i\sum_{\mathrm{i}=1}^{\infty}\left(\frac{4}{9}\right)^{\mathrm{i}}∑i=1∞​(94​)i

Find a general term, ana_{n}an​ , for the given terms of the sequence. - 6,14,22,30,38,…6,14,22,30,38, \ldots6,14,22,30,38,…

Find the sum, if it exists, of the terms of the infinite geometric sequence. - ∑i=1∞(−9),(−97))i\left.\sum_{i=1}^{\infty}(-9),\left(-\frac{9}{7}\right)\right)^{i}∑i=1∞​(−9),(−79​))i

Find the indicated term of the binomial expansion. - (4x−3y)11;10(4 x-3 y)^{11} ; 10(4x−3y)11;10 th term

In your own words, explain how to determine the binomial coefficient for x5y4x^{5} y^{4}x5y4 in the expansion of (x+y)9(x+y)^{9}(x+y)9 .

Find a4a_{4}a4​ for the sequence described. -Arithmetic, with a1=7a_{1}=7a1​=7 and d=−5d=-5d=−5

Find the indicated term for the geometric sequence. - a1=6,r=−2\mathrm{a}_{1}=6, \mathrm{r}=-2a1​=6,r=−2 ; a14\mathrm{a}_{14}a14​

Evaluate the series - ∑i=14(i2−4i−3)\sum_{i=1}^{4}\left(i^{2}-4 i-3\right)∑i=14​(i2−4i−3)

Find the requested sum for the arithmetic sequence. - an=−3n−9;S5a_{n}=-3 n-9 ; S_{5}an​=−3n−9;S5​

Write the first five terms of the sequence described -Arithmetic, with a1=23,d=7a_{1}=23, d=7a1​=23,d=7

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

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\mathrm{a}_{1}=7, \mathrm{r}=\frac{1}{5}$

Use the binomial theorem to expand the expression. - $(a-b)^{6}$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\mathrm{a}_{1}=5, \mathrm{r}=-\frac{1}{3}$

Find the indicated term for the sequence. - $\mathrm{a}_{\mathrm{n}}=\frac{2 \mathrm{n}-1}{3 \mathrm{n}+4} ; \mathrm{a}_{13}$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $0,2,6,12,20, \ldots$

The number of mutual funds available to investors in Dereguland for each year during 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?

Suppose you invest $\$ 8900$ at the end of each year into an account earning $6 \%$ interest (compounded annually). At the end of 6 years, how much money will be in the account?

$\frac{9 !}{6 ! 3 !}$

Use a formula for $S_{\mathbf{n}}$ to evaluate the series. - $\sum_{i=1}^{7532} i$

Find the sum if it exists. - $\sum_{\mathrm{i}=1}^{\infty}\left(\frac{4}{9}\right)^{\mathrm{i}}$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $6,14,22,30,38, \ldots$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\left.\sum_{i=1}^{\infty}(-9),\left(-\frac{9}{7}\right)\right)^{i}$

Find the indicated term of the binomial expansion. - $(4 x-3 y)^{11} ; 10$ th term

In your own words, explain how to determine the binomial coefficient for $x^{5} y^{4}$ in the expansion of $(x+y)^{9}$ .

Find $a_{4}$ for the sequence described. -Arithmetic, with $a_{1}=7$ and $d=-5$

Find the indicated term for the geometric sequence. - $\mathrm{a}_{1}=6, \mathrm{r}=-2$ ; $\mathrm{a}_{14}$

Evaluate the series - $\sum_{i=1}^{4}\left(i^{2}-4 i-3\right)$

Find the requested sum for the arithmetic sequence. - $a_{n}=-3 n-9 ; S_{5}$

Write the first five terms of the sequence described -Arithmetic, with $a_{1}=23, d=7$