Question 1

How do you determine the common ratio of a geometric sequence?

Accepted Answer

Divide any

Question 2

Write the first five terms of the arithmetic sequence.
-$a_{1}=6, d=4$

Accepted Answer

A)  $0,6,10,14,18$ 
B)  $6,9,12,15,18$ 
C)  $6,10,14,18,22$ 
D)  $10,14,18,22,27$ 
A)  $0,6,10,14,18$ 
B)  $6,9,12,15,18$ 
C)  $6,10,14,18,22$ 
D)  $10,14,18,22,27$

Question 3

Find the indicated term for the sequence.
-$a_{n}=(3 n-8)(2 n+8) ; a_{10}$

Accepted Answer

A)  616 
B)  384 
C)  494 
D)  750 
A)  616 
B)  384 
C)  494 
D)  750

Question 4

Find a general term for the geometric sequence.
-$\frac{1}{2}, \frac{1}{6}, \ldots$

Accepted Answer

A)  $a_{n}=\frac{1}{4 n-2}$ 
B)  $a_{n}=\frac{1}{3}\left(\frac{1}{2}\right)^{n-1}$ 
C)  $\mathrm{a}_{\mathrm{n}}=\frac{1}{2}\left(\frac{1}{3}\right)^{\mathrm{n}-1}$ 
D)  $\mathrm{a}_{\mathrm{n}}=\frac{1}{2}\left(\frac{1}{3}\right)^{1-\mathrm{n}}$ 
A)  $a_{n}=\frac{1}{4 n-2}$ 
B)  $a_{n}=\frac{1}{3}\left(\frac{1}{2}\right)^{n-1}$ 
C)  $\mathrm{a}_{\mathrm{n}}=\frac{1}{2}\left(\frac{1}{3}\right)^{\mathrm{n}-1}$ 
D)  $\mathrm{a}_{\mathrm{n}}=\frac{1}{2}\left(\frac{1}{3}\right)^{1-\mathrm{n}}$

Question 5

Write out the first five terms of the sequence.
-$a_{n}=n-\frac{4}{n}$

Accepted Answer

A)  $-1, \frac{7}{2}, \frac{14}{3}, \frac{23}{4},-\frac{2}{5}$ 
B)  $5,4, \frac{13}{3}, 5, \frac{29}{5}$ 
C)  $-3,-1,-\frac{1}{3}, 0, \frac{1}{5}$ 
D)  $-3,0, \frac{5}{3}, 3, \frac{21}{5}$ 
A)  $-1, \frac{7}{2}, \frac{14}{3}, \frac{23}{4},-\frac{2}{5}$ 
B)  $5,4, \frac{13}{3}, 5, \frac{29}{5}$ 
C)  $-3,-1,-\frac{1}{3}, 0, \frac{1}{5}$ 
D)  $-3,0, \frac{5}{3}, 3, \frac{21}{5}$

Question 6

Find the indicated term of the binomial expansion.
-The term with $x^{24}$ in $\left(x^{5}-\frac{5}{x}\right)^{6}$

Accepted Answer

A)  $75 x^{24}$ 
B)  $-30 x^{24}$ 
C)  $30 x^{24}$ 
D)  $-75 x^{24}$ 
A)  $75 x^{24}$ 
B)  $-30 x^{24}$ 
C)  $30 x^{24}$ 
D)  $-75 x^{24}$

Question 7

How many terms are in the expansion of $(x+y)^{11}$ ?

Accepted Answer

The answer of How many terms are in the expansion...

Question 8

Write the first five terms of the sequence described
-Geometric, with $\mathrm{a}_{4}=18$ and $\mathrm{r}=\frac{1}{3}$

Accepted Answer

A)  $81,27,9,3,1$ 
B)  $486,162,54,18,6$ 
C)  $162,54,18,6,2$ 
D)  $243,81,27,9,3$ 
A)  $81,27,9,3,1$ 
B)  $486,162,54,18,6$ 
C)  $162,54,18,6,2$ 
D)  $243,81,27,9,3$

Question 9

A rose garden has 16 bushes in the first row, 13 bushes in the next row, then 10 , and so on. If there are 51 bushes in the garden, in how many rows are they planted?

Accepted Answer

A)  7 
B)  5 
C)  6 
D)  3 
A)  7 
B)  5 
C)  6 
D)  3

Question 10

Write the first five terms of the arithmetic sequence.
-$a_{1}=21, d=7$

Accepted Answer

A)  $21,28,35,42,49$ 
B)  $21,7,56,84,112$ 
C)  $21,7,35,42,49$ 
D)  $7,28,49,70,91$ 
A)  $21,28,35,42,49$ 
B)  $21,7,56,84,112$ 
C)  $21,7,35,42,49$ 
D)  $7,28,49,70,91$

Question 11

Find the indicated term for the geometric sequence.
-$\mathrm{a}_{1}=-3, \mathrm{r}=4$; $\mathrm{a} 9$

Accepted Answer

A)  786,432 
B)  $3,145,728$ 
C)  $-196,608$ 
D)  $-65,536$ 
A)  786,432 
B)  $3,145,728$ 
C)  $-196,608$ 
D)  $-65,536$

Question 12

Write out the first five terms of the sequence.
-$a_{n}=n+\frac{1}{n}$

Accepted Answer

A)  $2, \frac{3}{2}, \frac{4}{3}, \frac{5}{4}, \frac{6}{5}$ 
B)  $1, \frac{3}{2}, \frac{4}{3}, \frac{5}{4}, \frac{6}{5}$ 
C)  $0,2, \frac{5}{2}, \frac{10}{3}, \frac{17}{4}$ 
D)  $2, \frac{5}{2}, \frac{10}{3}, \frac{17}{4}, \frac{26}{5}$ 
A)  $2, \frac{3}{2}, \frac{4}{3}, \frac{5}{4}, \frac{6}{5}$ 
B)  $1, \frac{3}{2}, \frac{4}{3}, \frac{5}{4}, \frac{6}{5}$ 
C)  $0,2, \frac{5}{2}, \frac{10}{3}, \frac{17}{4}$ 
D)  $2, \frac{5}{2}, \frac{10}{3}, \frac{17}{4}, \frac{26}{5}$

Question 13

Use a formula for $S_{\mathbf{n}}$ to evaluate the series.
-$\sum_{\mathrm{i}=1}^{6}\left(-\frac{5}{2} \mathrm{i}+3\right)$

Accepted Answer

A)  $-\frac{69}{2}$ 
B)  -12 
C)  -36 
D)  $-\frac{23}{2}$ 
A)  $-\frac{69}{2}$ 
B)  -12 
C)  -36 
D)  $-\frac{23}{2}$

Question 14

If $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \mathrm{a}_{4}, \mathrm{a}_{5}, \ldots$ is a geometric sequence with common ratio $\mathrm{r}$, show that $\mathrm{a}_{1}, \mathrm{a}_{4}, \mathrm{a}_{7}$, a10 is a geometric sequence.

Accepted Answer

Answers will vary. T

Question 15

Explain how to find the common difference for an arithmetic sequence if you are given a39 and $\mathrm{a}_{40}$.

Accepted Answer

The common

Question 16

Find the number of terms in the arithmetic sequence.
-$-7,1,9, \ldots, 177$

Accepted Answer

A)  24 
B)  25 
C)  23 
D)  22 
A)  24 
B)  25 
C)  23 
D)  22

Question 17

Write the first five terms of the geometric sequence.
-$\mathrm{a}_{1}=-3, \mathrm{r}=-\frac{1}{11}$

Accepted Answer

A)  $-3,-\frac{3}{11},-\frac{3}{121},-\frac{3}{1331},-\frac{3}{14641}$ 
B) $-3,-33,-363,-3993,-43,923$ 
C)  $-3,33,-363,3993,-43,923$ 
D)  $-3, \frac{3}{11},-\frac{3}{121}, \frac{3}{1331},-\frac{3}{14641}$ 
A)  $-3,-\frac{3}{11},-\frac{3}{121},-\frac{3}{1331},-\frac{3}{14641}$ 
B) $-3,-33,-363,-3993,-43,923$ 
C)  $-3,33,-363,3993,-43,923$ 
D)  $-3, \frac{3}{11},-\frac{3}{121}, \frac{3}{1331},-\frac{3}{14641}$

Question 18

Find the sum if it exists.
-$\sum_{\mathrm{i}=1}^{580} \mathrm{i}$

Accepted Answer

A)  167,910 
B)  581 
C)  168,490 
D)  579 
A)  167,910 
B)  581 
C)  168,490 
D)  579

Question 19

Write the first five terms of the geometric sequence.
-$\mathrm{a}_{1}=7, \mathrm{r}=-7$

Accepted Answer

A)  $7,49,343,2401,16,807$ 
B)  $-49,343,-2401,16,807,-117,649$ 
C)  $7,0,-7,-14,-21$ 
D)  $7,-49,343,-2401,16,807$ 
A)  $7,49,343,2401,16,807$ 
B)  $-49,343,-2401,16,807,-117,649$ 
C)  $7,0,-7,-14,-21$ 
D)  $7,-49,343,-2401,16,807$

Question 20

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

Accepted Answer

A)  81 
B)  $225 \mathrm{x}^{2}$ 
C)  $405 x$ 
D)  $135 x$ 
A)  81 
B)  $225 \mathrm{x}^{2}$ 
C)  $405 x$ 
D)  $135 x$

How do you determine the common ratio of a geometric sequence?

Write the first five terms of the arithmetic sequence. - $a_{1}=6, d=4$

Find the indicated term for the sequence. - $a_{n}=(3 n-8)(2 n+8) ; a_{10}$

Find a general term for the geometric sequence. - $\frac{1}{2}, \frac{1}{6}, \ldots$

Write out the first five terms of the sequence. - $a_{n}=n-\frac{4}{n}$

Find the indicated term of the binomial expansion. -The term with $x^{24}$ in $\left(x^{5}-\frac{5}{x}\right)^{6}$

How many terms are in the expansion of $(x+y)^{11}$ ?

Write the first five terms of the sequence described -Geometric, with $\mathrm{a}_{4}=18$ and $\mathrm{r}=\frac{1}{3}$

A rose garden has 16 bushes in the first row, 13 bushes in the next row, then 10 , and so on. If there are 51 bushes in the garden, in how many rows are they planted?

Write the first five terms of the arithmetic sequence. - $a_{1}=21, d=7$

Find the indicated term for the geometric sequence. - $\mathrm{a}_{1}=-3, \mathrm{r}=4$ ; $\mathrm{a} 9$

Write out the first five terms of the sequence. - $a_{n}=n+\frac{1}{n}$

Use a formula for $S_{\mathbf{n}}$ to evaluate the series. - $\sum_{\mathrm{i}=1}^{6}\left(-\frac{5}{2} \mathrm{i}+3\right)$

If $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \mathrm{a}_{4}, \mathrm{a}_{5}, \ldots$ is a geometric sequence with common ratio $\mathrm{r}$ , show that $\mathrm{a}_{1}, \mathrm{a}_{4}, \mathrm{a}_{7}$ , a10 is a geometric sequence.

Explain how to find the common difference for an arithmetic sequence if you are given a39 and $\mathrm{a}_{40}$ .

Find the number of terms in the arithmetic sequence. - $-7,1,9, \ldots, 177$

Write the first five terms of the geometric sequence. - $\mathrm{a}_{1}=-3, \mathrm{r}=-\frac{1}{11}$

Find the sum if it exists. - $\sum_{\mathrm{i}=1}^{580} \mathrm{i}$

Write the first five terms of the geometric sequence. - $\mathrm{a}_{1}=7, \mathrm{r}=-7$

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

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

How do you determine the common ratio of a geometric sequence?

Write the first five terms of the arithmetic sequence. - a1=6,d=4a_{1}=6, d=4a1​=6,d=4

Find the indicated term for the sequence. - an=(3n−8)(2n+8);a10a_{n}=(3 n-8)(2 n+8) ; a_{10}an​=(3n−8)(2n+8);a10​

Find a general term for the geometric sequence. - 12,16,…\frac{1}{2}, \frac{1}{6}, \ldots21​,61​,…

Write out the first five terms of the sequence. - an=n−4na_{n}=n-\frac{4}{n}an​=n−n4​

Find the indicated term of the binomial expansion. -The term with x24x^{24}x24 in (x5−5x)6\left(x^{5}-\frac{5}{x}\right)^{6}(x5−x5​)6

How many terms are in the expansion of (x+y)11(x+y)^{11}(x+y)11 ?

Write the first five terms of the sequence described -Geometric, with a4=18\mathrm{a}_{4}=18a4​=18 and r=13\mathrm{r}=\frac{1}{3}r=31​

A rose garden has 16 bushes in the first row, 13 bushes in the next row, then 10 , and so on. If there are 51 bushes in the garden, in how many rows are they planted?

Write the first five terms of the arithmetic sequence. - a1=21,d=7a_{1}=21, d=7a1​=21,d=7

Find the indicated term for the geometric sequence. - a1=−3,r=4\mathrm{a}_{1}=-3, \mathrm{r}=4a1​=−3,r=4 ; a9\mathrm{a} 9a9

Write out the first five terms of the sequence. - an=n+1na_{n}=n+\frac{1}{n}an​=n+n1​

Use a formula for SnS_{\mathbf{n}}Sn​ to evaluate the series. - ∑i=16(−52i+3)\sum_{\mathrm{i}=1}^{6}\left(-\frac{5}{2} \mathrm{i}+3\right)∑i=16​(−25​i+3)

Explain how to find the common difference for an arithmetic sequence if you are given a39 and a40\mathrm{a}_{40}a40​ .

Find the number of terms in the arithmetic sequence. - −7,1,9,…,177-7,1,9, \ldots, 177−7,1,9,…,177

Write the first five terms of the geometric sequence. - a1=−3,r=−111\mathrm{a}_{1}=-3, \mathrm{r}=-\frac{1}{11}a1​=−3,r=−111​

Find the sum if it exists. - ∑i=1580i\sum_{\mathrm{i}=1}^{580} \mathrm{i}∑i=1580​i

Write the first five terms of the geometric sequence. - a1=7,r=−7\mathrm{a}_{1}=7, \mathrm{r}=-7a1​=7,r=−7

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

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 first five terms of the arithmetic sequence. - $a_{1}=6, d=4$

Find the indicated term for the sequence. - $a_{n}=(3 n-8)(2 n+8) ; a_{10}$

Find a general term for the geometric sequence. - $\frac{1}{2}, \frac{1}{6}, \ldots$

Write out the first five terms of the sequence. - $a_{n}=n-\frac{4}{n}$

Find the indicated term of the binomial expansion. -The term with $x^{24}$ in $\left(x^{5}-\frac{5}{x}\right)^{6}$

How many terms are in the expansion of $(x+y)^{11}$ ?

Write the first five terms of the sequence described -Geometric, with $\mathrm{a}_{4}=18$ and $\mathrm{r}=\frac{1}{3}$

Write the first five terms of the arithmetic sequence. - $a_{1}=21, d=7$

Find the indicated term for the geometric sequence. - $\mathrm{a}_{1}=-3, \mathrm{r}=4$ ; $\mathrm{a} 9$

Write out the first five terms of the sequence. - $a_{n}=n+\frac{1}{n}$

Use a formula for $S_{\mathbf{n}}$ to evaluate the series. - $\sum_{\mathrm{i}=1}^{6}\left(-\frac{5}{2} \mathrm{i}+3\right)$

Explain how to find the common difference for an arithmetic sequence if you are given a39 and $\mathrm{a}_{40}$ .

Find the number of terms in the arithmetic sequence. - $-7,1,9, \ldots, 177$

Write the first five terms of the geometric sequence. - $\mathrm{a}_{1}=-3, \mathrm{r}=-\frac{1}{11}$

Find the sum if it exists. - $\sum_{\mathrm{i}=1}^{580} \mathrm{i}$

Write the first five terms of the geometric sequence. - $\mathrm{a}_{1}=7, \mathrm{r}=-7$

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