Question 1

Write the series with summation notation.
-$-2+3-4+5-6+7$

Accepted Answer

A)  $\sum_{\mathrm{i}=1}^{6}(-1)^{\mathrm{i}} \cdot(\mathrm{i}+1)$ 
B)  $\sum_{i=1}^{6}(-1)^{i+1} \cdot(i+1)$ 
C)  $\sum_{i=1}^{6}(-1)^{\mathrm{i}+1} \cdot(\mathrm{i}+2)$ 
D)  $\sum_{i=1}^{6}(-1)^{\mathrm{i}} \cdot(\mathrm{i}+2)$ 
A)  $\sum_{\mathrm{i}=1}^{6}(-1)^{\mathrm{i}} \cdot(\mathrm{i}+1)$ 
B)  $\sum_{i=1}^{6}(-1)^{i+1} \cdot(i+1)$ 
C)  $\sum_{i=1}^{6}(-1)^{\mathrm{i}+1} \cdot(\mathrm{i}+2)$ 
D)  $\sum_{i=1}^{6}(-1)^{\mathrm{i}} \cdot(\mathrm{i}+2)$ A

Question 2

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence.
-$\frac{2}{3}, \frac{4}{3}, \frac{8}{3}, \frac{16}{3}, \frac{32}{3}$

Accepted Answer

A)  $\frac{62}{3}$ 
B)  $\frac{64}{3}$ 
C)  21 
D)  $\frac{60}{3}$ 
A)  $\frac{62}{3}$ 
B)  $\frac{64}{3}$ 
C)  21 
D)  $\frac{60}{3}$ A

Question 3

Use the binomial theorem to expand the expression.
-$(5 x-5 y)^{3}$

Accepted Answer

A)  $25 x^{3} y-50 x^{2} y^{2}+25 x y^{3}$ 
B)  $125 x^{3}-375 x^{2} y+375 x y^{2}-125 y^{3}$ 
C)  $125 x^{3}-125 x^{2} y+125 x y^{2}-125 y^{3}$ 
D)  $25 x^{3} y-25 x^{2} y^{2}+25 x y^{3}$ 
A)  $25 x^{3} y-50 x^{2} y^{2}+25 x y^{3}$ 
B)  $125 x^{3}-375 x^{2} y+375 x y^{2}-125 y^{3}$ 
C)  $125 x^{3}-125 x^{2} y+125 x y^{2}-125 y^{3}$ 
D)  $25 x^{3} y-25 x^{2} y^{2}+25 x y^{3}$ B

Question 4

Find a general term, $a_{n}$, for the given terms of the sequence.
-$\frac{2}{7}, \frac{3}{8}, \frac{4}{9}, \frac{5}{10}, \ldots$

Accepted Answer

A)  $a_{n}=\frac{n+1}{n+6}$ 
B)  $a_{n}=\frac{n+1}{n^{6}}$ 
C)  $a_{n}=\frac{n}{n-6}$ 
D)  $a_{n}=\frac{n}{n+6}$ 
A)  $a_{n}=\frac{n+1}{n+6}$ 
B)  $a_{n}=\frac{n+1}{n^{6}}$ 
C)  $a_{n}=\frac{n}{n-6}$ 
D)  $a_{n}=\frac{n}{n+6}$

Question 5

Find the indicated term of the binomial expansion.
-$(x-2 y)^{13}$; 11 th term

Accepted Answer

A)  $292,864 x^{10} y^{3}$ 
B)  $-146,432 x^{10} y^{3}$ 
C)  $292,864 x^{3} y^{10}$ 
D)  $-146,432 x^{3} y^{11}$ 
A)  $292,864 x^{10} y^{3}$ 
B)  $-146,432 x^{10} y^{3}$ 
C)  $292,864 x^{3} y^{10}$ 
D)  $-146,432 x^{3} y^{11}$

Question 6

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence.
-$\sum_{\mathrm{i}=1}^{5} 3(-4)^{\mathrm{i}}$

Accepted Answer

A)  244 
B)  -156 
C)  -2460 
D)  -7710 
A)  244 
B)  -156 
C)  -2460 
D)  -7710

Question 7

Find the indicated term for the sequence.
-$\mathrm{a}_{\mathrm{n}}=4^{\mathrm{n}}$; $\mathrm{a}_{3}$

Accepted Answer

A)  64 
B)  12 
C)  16 
D)  81 
A)  64 
B)  12 
C)  16 
D)  81

Question 8

Evaluate the expression
-${ }_{9} \mathrm{C}_{5}$

Accepted Answer

A)  3024 
B)  15,120 
C)  126 
D)  181,440 
A)  3024 
B)  15,120 
C)  126 
D)  181,440

Question 9

Write the first five terms of the sequence described
-$\mathrm{a}_{\mathrm{n}}=(-1)^{\mathrm{n}}+13$

Accepted Answer

A)  $12,-14,12,-14,12$ 
B)  $12,14,12,14,12$ 
C)  $14,12,14,12,14$ 
D)  $-13,13,-13,13,-13$ 
A)  $12,-14,12,-14,12$ 
B)  $12,14,12,14,12$ 
C)  $14,12,14,12,14$ 
D)  $-13,13,-13,13,-13$

Question 10

Find $\mathrm{S}_{5}$ for the sequence described.
-Arithmetic, with $\mathrm{a}_{2}=18$ and $\mathrm{a}_{3}=22$

Accepted Answer

A)  70 
B)  110 
C)  106 
D)  38 
A)  70 
B)  110 
C)  106 
D)  38

Question 11

Write out the first five terms of the sequence.
-$a_{n}=\frac{n}{n+3}$

Accepted Answer

A)  $\frac{1}{4}, \frac{2}{5}, \frac{1}{2}, \frac{4}{7}, \frac{5}{8}$ 
B)  $\frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, 0$ 
C)  $\frac{1}{4}, \frac{2}{5}, \frac{1}{2}, \frac{4}{7}, \frac{11}{7}$ 
D)  $0, \frac{1}{4}, \frac{2}{5}, \frac{1}{2}, \frac{4}{7}$ 
A)  $\frac{1}{4}, \frac{2}{5}, \frac{1}{2}, \frac{4}{7}, \frac{5}{8}$ 
B)  $\frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, 0$ 
C)  $\frac{1}{4}, \frac{2}{5}, \frac{1}{2}, \frac{4}{7}, \frac{11}{7}$ 
D)  $0, \frac{1}{4}, \frac{2}{5}, \frac{1}{2}, \frac{4}{7}$

Question 12

A man borrowed $\$ 1000$ at $10 \%$ interest compounded annually. If he paid off the loan in full at the end of 6 years, how much did he pay? Round your answer to the nearest cent.

Accepted Answer

A)  $\$ 1100.00$ 
B)  $\$ 771.56$ 
C)  $\$ 1771.56$ 
D)  $\$ 1600.00$ 
A)  $\$ 1100.00$ 
B)  $\$ 771.56$ 
C)  $\$ 1771.56$ 
D)  $\$ 1600.00$

Question 13

Write the first five terms of the geometric sequence.
-$\mathrm{a}_{1}=128, \mathrm{r}=\frac{1}{2}$

Accepted Answer

A)  $64,32,16,8,4$ 
B)  $4,8,16,32,64$ 
C)  $8,16,32,64,128$ 
D)  $128,64,32,16,8$ 
A)  $64,32,16,8,4$ 
B)  $4,8,16,32,64$ 
C)  $8,16,32,64,128$ 
D)  $128,64,32,16,8$

Question 14

Evaluate the series
-$\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}$

Accepted Answer

A)  $\frac{6}{7}$ 
B)  $\frac{21}{10}$ 
C)  $\frac{61}{20}$ 
D)  $\frac{71}{20}$ 
A)  $\frac{6}{7}$ 
B)  $\frac{21}{10}$ 
C)  $\frac{61}{20}$ 
D)  $\frac{71}{20}$

Question 15

If a person puts one penny in a piggy bank on the first day, two pennies in on the second day, three pennies in on the third day, and so forth, how much money will be in the bank after 30 days?

Accepted Answer

A)  $\$ 9.30$ 
B)  $\$ 0.30$ 
C)  $\$ 4.65$ 
D)  $\$ 2.33$ 
A)  $\$ 9.30$ 
B)  $\$ 0.30$ 
C)  $\$ 4.65$ 
D)  $\$ 2.33$

Question 16

Find a general term, $a_{n}$, for the given terms of the sequence.
-$-4,-8,-12,-16,-20, \ldots$

Accepted Answer

A)  $a_{n}=-4 n+1$ 
B)  $a_{n}=-\frac{1}{4}$ 
C)  $a_{n}=-4 n$ 
D)  $\mathrm{a}_{\mathrm{n}}=4 \mathrm{n}$ 
A)  $a_{n}=-4 n+1$ 
B)  $a_{n}=-\frac{1}{4}$ 
C)  $a_{n}=-4 n$ 
D)  $\mathrm{a}_{\mathrm{n}}=4 \mathrm{n}$

Question 17

Write the first five terms of the geometric sequence.
-$\mathrm{a}_{1}=-5, \mathrm{r}=-4$

Accepted Answer

A)  $5,1,-3,-7,-11$ 
B)  $-5,20,-80,320,-1280$ 
C)  $-5,-20,-80,-320,-1280$ 
D)  $5,-20,80,-320,1280$ 
A)  $5,1,-3,-7,-11$ 
B)  $-5,20,-80,320,-1280$ 
C)  $-5,-20,-80,-320,-1280$ 
D)  $5,-20,80,-320,1280$

Question 18

Find the indicated term for the arithmetic sequence.
-$a_{1}=-2, d=3$; $a_{8}$

Accepted Answer

A)  -23 
B)  22 
C)  -26 
D)  19 
A)  -23 
B)  22 
C)  -26 
D)  19

Question 19

Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\sum_{\mathrm{i}=1}^{\infty}(2)\left(\frac{1}{3}\right)^{\mathrm{i}}$

Accepted Answer

A)  $\frac{3}{2}$ 
B)  2 
C)  1 
D)  Does not exist 
A)  $\frac{3}{2}$ 
B)  2 
C)  1 
D)  Does not exist

Question 20

Mona bought a computer for $\$ 200$. She agreed to pay $\$ 50$ per month for 4 months, plus $2 \%$ interest, on the unpaid balance. Find the total cost of the computer.

Accepted Answer

A)  $\$ 190$ 
B)  $\$ 208$ 
C)  $\$ 210$ 
D)  $\$ 206$ 
A)  $\$ 190$ 
B)  $\$ 208$ 
C)  $\$ 210$ 
D)  $\$ 206$

Write the series with summation notation. - $-2+3-4+5-6+7$

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence. - $\frac{2}{3}, \frac{4}{3}, \frac{8}{3}, \frac{16}{3}, \frac{32}{3}$

Use the binomial theorem to expand the expression. - $(5 x-5 y)^{3}$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $\frac{2}{7}, \frac{3}{8}, \frac{4}{9}, \frac{5}{10}, \ldots$

Find the indicated term of the binomial expansion. - $(x-2 y)^{13}$ ; 11 th term

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence. - $\sum_{\mathrm{i}=1}^{5} 3(-4)^{\mathrm{i}}$

Find the indicated term for the sequence. - $\mathrm{a}_{\mathrm{n}}=4^{\mathrm{n}}$ ; $\mathrm{a}_{3}$

Evaluate the expression - ${ }_{9} \mathrm{C}_{5}$

Write the first five terms of the sequence described - $\mathrm{a}_{\mathrm{n}}=(-1)^{\mathrm{n}}+13$

Find $\mathrm{S}_{5}$ for the sequence described. -Arithmetic, with $\mathrm{a}_{2}=18$ and $\mathrm{a}_{3}=22$

Write out the first five terms of the sequence. - $a_{n}=\frac{n}{n+3}$

A man borrowed $\$ 1000$ at $10 \%$ interest compounded annually. If he paid off the loan in full at the end of 6 years, how much did he pay? Round your answer to the nearest cent.

Write the first five terms of the geometric sequence. - $\mathrm{a}_{1}=128, \mathrm{r}=\frac{1}{2}$

Evaluate the series - $\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}$

If a person puts one penny in a piggy bank on the first day, two pennies in on the second day, three pennies in on the third day, and so forth, how much money will be in the bank after 30 days?

Find a general term, $a_{n}$ , for the given terms of the sequence. - $-4,-8,-12,-16,-20, \ldots$

Write the first five terms of the geometric sequence. - $\mathrm{a}_{1}=-5, \mathrm{r}=-4$

Find the indicated term for the arithmetic sequence. - $a_{1}=-2, d=3$ ; $a_{8}$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\sum_{\mathrm{i}=1}^{\infty}(2)\left(\frac{1}{3}\right)^{\mathrm{i}}$

Mona bought a computer for $\$ 200$ . She agreed to pay $\$ 50$ per month for 4 months, plus $2 \%$ interest, on the unpaid balance. Find the total cost of the computer.

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 the series with summation notation. - −2+3−4+5−6+7-2+3-4+5-6+7−2+3−4+5−6+7

Use the formula for Sn\mathbf{S}_{\mathbf{n}}Sn​ to find the sum for the geometric sequence. - 23,43,83,163,323\frac{2}{3}, \frac{4}{3}, \frac{8}{3}, \frac{16}{3}, \frac{32}{3}32​,34​,38​,316​,332​

Use the binomial theorem to expand the expression. - (5x−5y)3(5 x-5 y)^{3}(5x−5y)3

Find a general term, ana_{n}an​ , for the given terms of the sequence. - 27,38,49,510,…\frac{2}{7}, \frac{3}{8}, \frac{4}{9}, \frac{5}{10}, \ldots72​,83​,94​,105​,…

Find the indicated term of the binomial expansion. - (x−2y)13(x-2 y)^{13}(x−2y)13 ; 11 th term

Use the formula for Sn\mathbf{S}_{\mathbf{n}}Sn​ to find the sum for the geometric sequence. - ∑i=153(−4)i\sum_{\mathrm{i}=1}^{5} 3(-4)^{\mathrm{i}}∑i=15​3(−4)i

Find the indicated term for the sequence. - an=4n\mathrm{a}_{\mathrm{n}}=4^{\mathrm{n}}an​=4n ; a3\mathrm{a}_{3}a3​

Evaluate the expression - 9C5{ }_{9} \mathrm{C}_{5}9​C5​

Write the first five terms of the sequence described - an=(−1)n+13\mathrm{a}_{\mathrm{n}}=(-1)^{\mathrm{n}}+13an​=(−1)n+13

Find S5\mathrm{S}_{5}S5​ for the sequence described. -Arithmetic, with a2=18\mathrm{a}_{2}=18a2​=18 and a3=22\mathrm{a}_{3}=22a3​=22

Write out the first five terms of the sequence. - an=nn+3a_{n}=\frac{n}{n+3}an​=n+3n​

A man borrowed $1000\$ 1000$1000 at 10%10 \%10% interest compounded annually. If he paid off the loan in full at the end of 6 years, how much did he pay? Round your answer to the nearest cent.

Write the first five terms of the geometric sequence. - a1=128,r=12\mathrm{a}_{1}=128, \mathrm{r}=\frac{1}{2}a1​=128,r=21​

Evaluate the series - ∑i=14i+1i+2\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}∑i=14​i+2i+1​

If a person puts one penny in a piggy bank on the first day, two pennies in on the second day, three pennies in on the third day, and so forth, how much money will be in the bank after 30 days?

Find a general term, ana_{n}an​ , for the given terms of the sequence. - −4,−8,−12,−16,−20,…-4,-8,-12,-16,-20, \ldots−4,−8,−12,−16,−20,…

Write the first five terms of the geometric sequence. - a1=−5,r=−4\mathrm{a}_{1}=-5, \mathrm{r}=-4a1​=−5,r=−4

Find the indicated term for the arithmetic sequence. - a1=−2,d=3a_{1}=-2, d=3a1​=−2,d=3 ; a8a_{8}a8​

Find the sum, if it exists, of the terms of the infinite geometric sequence. - ∑i=1∞(2)(13)i\sum_{\mathrm{i}=1}^{\infty}(2)\left(\frac{1}{3}\right)^{\mathrm{i}}∑i=1∞​(2)(31​)i

Mona bought a computer for $200\$ 200$200 . She agreed to pay $50\$ 50$50 per month for 4 months, plus 2%2 \%2% interest, on the unpaid balance. Find the total cost of the computer.

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 the series with summation notation. - $-2+3-4+5-6+7$

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence. - $\frac{2}{3}, \frac{4}{3}, \frac{8}{3}, \frac{16}{3}, \frac{32}{3}$

Use the binomial theorem to expand the expression. - $(5 x-5 y)^{3}$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $\frac{2}{7}, \frac{3}{8}, \frac{4}{9}, \frac{5}{10}, \ldots$

Find the indicated term of the binomial expansion. - $(x-2 y)^{13}$ ; 11 th term

Use the formula for $\mathbf{S}_{\mathbf{n}}$ to find the sum for the geometric sequence. - $\sum_{\mathrm{i}=1}^{5} 3(-4)^{\mathrm{i}}$

Find the indicated term for the sequence. - $\mathrm{a}_{\mathrm{n}}=4^{\mathrm{n}}$ ; $\mathrm{a}_{3}$

Evaluate the expression - ${ }_{9} \mathrm{C}_{5}$

Write the first five terms of the sequence described - $\mathrm{a}_{\mathrm{n}}=(-1)^{\mathrm{n}}+13$

Find $\mathrm{S}_{5}$ for the sequence described. -Arithmetic, with $\mathrm{a}_{2}=18$ and $\mathrm{a}_{3}=22$

Write out the first five terms of the sequence. - $a_{n}=\frac{n}{n+3}$

A man borrowed $\$ 1000$ at $10 \%$ interest compounded annually. If he paid off the loan in full at the end of 6 years, how much did he pay? Round your answer to the nearest cent.

Write the first five terms of the geometric sequence. - $\mathrm{a}_{1}=128, \mathrm{r}=\frac{1}{2}$

Evaluate the series - $\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $-4,-8,-12,-16,-20, \ldots$

Write the first five terms of the geometric sequence. - $\mathrm{a}_{1}=-5, \mathrm{r}=-4$

Find the indicated term for the arithmetic sequence. - $a_{1}=-2, d=3$ ; $a_{8}$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\sum_{\mathrm{i}=1}^{\infty}(2)\left(\frac{1}{3}\right)^{\mathrm{i}}$

Mona bought a computer for $\$ 200$ . She agreed to pay $\$ 50$ per month for 4 months, plus $2 \%$ interest, on the unpaid balance. Find the total cost of the computer.