Question 1

Find the arithmetic mean for the collection of numbers.
$11,7,5,14,9,8,17$

Accepted Answer

A)  $\frac{62}{7}$ 
B)  $\frac{71}{7}$ 
C)  $\frac{78}{7}$ 
D)  10 
A)  $\frac{62}{7}$ 
B)  $\frac{71}{7}$ 
C)  $\frac{78}{7}$ 
D)  10

Question 2

1!

Accepted Answer

A)  2 
B)  0 
C)  1 
D)  Undefined 
A)  2 
B)  0 
C)  1 
D)  Undefined

Question 3

Find $a_{4}$ for the sequence described.
-Geometric, with $a_{5}=100$ and $a_{7}=1$

Accepted Answer

A)  10 or -10 
B)  1000 or -1000 
C)  100 or -100 
D)  $\frac{1}{1000}$ or $-\frac{1}{1000}$ 
A)  10 or -10 
B)  1000 or -1000 
C)  100 or -100 
D)  $\frac{1}{1000}$ or $-\frac{1}{1000}$

Question 4

Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\sum_{\mathrm{i}=1}^{\infty} \frac{5}{3} \cdot\left(-\frac{1}{3}\right)^{\mathrm{i}-1}$

Accepted Answer

A)  $\frac{5}{4}$ 
B)  $\frac{5}{3}$ 
C)  $\frac{1}{4}$ 
D)  Does not exist 
A)  $\frac{5}{4}$ 
B)  $\frac{5}{3}$ 
C)  $\frac{1}{4}$ 
D)  Does not exist

Question 5

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so
-$1,-1,3,-5, \ldots$

Accepted Answer

A)  2 
B)  1 
C)  -1 
D)  Not geometric 
A)  2 
B)  1 
C)  -1 
D)  Not geometric

Question 6

Write the series with summation notation.
-$7+12+17+22+27$

Accepted Answer

A)  $\sum_{\mathrm{i}=1}^{5}(\mathrm{i}+2)$ 
B)  $\sum_{i=1}^{5} 5 \mathrm{i}$ 
C)  $\sum_{i=1}^{5}(5 i+2)$ 
D)  $\sum_{i=1}^{4}(5 i+2)$ 
A)  $\sum_{\mathrm{i}=1}^{5}(\mathrm{i}+2)$ 
B)  $\sum_{i=1}^{5} 5 \mathrm{i}$ 
C)  $\sum_{i=1}^{5}(5 i+2)$ 
D)  $\sum_{i=1}^{4}(5 i+2)$

Question 7

Find the indicated term for the arithmetic sequence.
-$\mathrm{a}_{11}=-41, \mathrm{a}_{19}=-81 ; \mathrm{a}_{7}$

Accepted Answer

A)  -26 
B)  -5 
C)  -21 
D)  9 
A)  -26 
B)  -5 
C)  -21 
D)  9

Question 8

Find $\mathrm{S}_{5}$ for the sequence described.
-Geometric, with $a_{5}=48$ and a $7=12$

Accepted Answer

A)  720 or 272 
B)  372 or 132 
C)  744 or 264 
D)  1488 or 528 
A)  720 or 272 
B)  372 or 132 
C)  744 or 264 
D)  1488 or 528

Question 9

Find a general term, $a_{n}$, for the given terms of the sequence.
-$\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \frac{5}{16}, \frac{5}{32}, \ldots$

Accepted Answer

A)  $a_{n}=\frac{5}{2 n}$ 
B)  $a_{n}=\frac{2}{5^{n}}$ 
C)  $a_{n}=\frac{5}{2^{n}}$ 
D)  $a_{n}=\frac{2}{5 n}$ 
A)  $a_{n}=\frac{5}{2 n}$ 
B)  $a_{n}=\frac{2}{5^{n}}$ 
C)  $a_{n}=\frac{5}{2^{n}}$ 
D)  $a_{n}=\frac{2}{5 n}$

Question 10

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

Accepted Answer

A)  108 
B)  1728 
C)  $\frac{4}{27}$ 
D)  27 
A)  108 
B)  1728 
C)  $\frac{4}{27}$ 
D)  27

Question 11

Find the indicated term for the sequence.
-$a_{n}=n^{2}-n$; ag

Accepted Answer

A)  -72 
B)  72 
C)  90 
D)  9 
A)  -72 
B)  72 
C)  90 
D)  9

Question 12

Evaluate the expression
-$\frac{3 !}{0 ! 3 !}$

Accepted Answer

A)  3 
B)  0 
C)  1 
D)  6 
A)  3 
B)  0 
C)  1 
D)  6

Question 13

If $\$ 1400$ is deposited in an ordinary annuity at the end of each quarter for $4 \mathrm{yr}$ and earns $3 \%$ interest compounded quarterly, how much will be in the account at the end of this term?

Accepted Answer

A)  $\$ 23,705.19$ 
B)  $\$ 5926.3$ 
C)  $\$ 112,878.54$ 
D)  $\$ 23,428.31$ 
A)  $\$ 23,705.19$ 
B)  $\$ 5926.3$ 
C)  $\$ 112,878.54$ 
D)  $\$ 23,428.31$

Question 14

Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\sum_{\mathrm{i}=1}^{\infty}(3)\left(-\frac{1}{4}\right)^{\mathrm{i}}$

Accepted Answer

A)  $\frac{3}{5}$ 
B)  $-\frac{3}{5}$ 
C)  -1 
D)  Does not exist 
A)  $\frac{3}{5}$ 
B)  $-\frac{3}{5}$ 
C)  -1 
D)  Does not exist

Question 15

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

Accepted Answer

A)  122 
B)  118 
C)  121 
D)  111 
A)  122 
B)  118 
C)  121 
D)  111

Question 16

Find the indicated term for the geometric sequence.
-$\mathrm{a}_{5}=-\frac{1}{4}, \mathrm{a}_{8}=\frac{1}{32} ; \mathrm{a}_{15}$

Accepted Answer

A)  $\frac{1}{8192}$ 
B)  $\frac{1}{4096}$ 
C)  $-\frac{1}{4096}$ 
D)  $-\frac{1}{8192}$ 
A)  $\frac{1}{8192}$ 
B)  $\frac{1}{4096}$ 
C)  $-\frac{1}{4096}$ 
D)  $-\frac{1}{8192}$

Question 17

The population of a town was 27,000 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Accepted Answer

A)  4500 
B)  22,800 
C)  22,200 
D)  22,500 
A)  4500 
B)  22,800 
C)  22,200 
D)  22,500

Question 18

Find the requested sum for the arithmetic sequence.
-$a_{n}=-5 n+8 ; S_{5}$

Accepted Answer

A)  -17 
B)  -35 
C)  15 
D)  -23 
A)  -17 
B)  -35 
C)  15 
D)  -23

Question 19

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence.
-$\mathrm{a}_{1}=4, \mathrm{~d}=-4$

Accepted Answer

A)  $a_{n}=4 n+4$ 
B)  $a_{n}=-4 n+8$ 
C)  $a_{n}=4 n-4$ 
D)  $a_{n}=-4 n-4$ 
A)  $a_{n}=4 n+4$ 
B)  $a_{n}=-4 n+8$ 
C)  $a_{n}=4 n-4$ 
D)  $a_{n}=-4 n-4$

Question 20

Write the first five terms of the arithmetic sequence.
-$a_{1}=7, d=-2$

Accepted Answer

A)  $9,7,5,3,1$ 
B)  $7,5,3,1,-1$ 
C)  $7,5,2,1,-1$ 
D)  $5,3,1,-1,-3$ 
A)  $9,7,5,3,1$ 
B)  $7,5,3,1,-1$ 
C)  $7,5,2,1,-1$ 
D)  $5,3,1,-1,-3$

Find the arithmetic mean for the collection of numbers. $11,7,5,14,9,8,17$

1!

Find $a_{4}$ for the sequence described. -Geometric, with $a_{5}=100$ and $a_{7}=1$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\sum_{\mathrm{i}=1}^{\infty} \frac{5}{3} \cdot\left(-\frac{1}{3}\right)^{\mathrm{i}-1}$

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $1,-1,3,-5, \ldots$

Write the series with summation notation. - $7+12+17+22+27$

Find the indicated term for the arithmetic sequence. - $\mathrm{a}_{11}=-41, \mathrm{a}_{19}=-81 ; \mathrm{a}_{7}$

Find $\mathrm{S}_{5}$ for the sequence described. -Geometric, with $a_{5}=48$ and a $7=12$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \frac{5}{16}, \frac{5}{32}, \ldots$

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

Find the indicated term for the sequence. - $a_{n}=n^{2}-n$ ; ag

Evaluate the expression - $\frac{3 !}{0 ! 3 !}$

If $\$ 1400$ is deposited in an ordinary annuity at the end of each quarter for $4 \mathrm{yr}$ and earns $3 \%$ interest compounded quarterly, how much will be in the account at the end of this term?

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\sum_{\mathrm{i}=1}^{\infty}(3)\left(-\frac{1}{4}\right)^{\mathrm{i}}$

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

Find the indicated term for the geometric sequence. - $\mathrm{a}_{5}=-\frac{1}{4}, \mathrm{a}_{8}=\frac{1}{32} ; \mathrm{a}_{15}$

The population of a town was 27,000 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Find the requested sum for the arithmetic sequence. - $a_{n}=-5 n+8 ; S_{5}$

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence. - $\mathrm{a}_{1}=4, \mathrm{~d}=-4$

Write the first five terms of the arithmetic sequence. - $a_{1}=7, d=-2$

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 arithmetic mean for the collection of numbers. 11,7,5,14,9,8,1711,7,5,14,9,8,1711,7,5,14,9,8,17

1!

Find a4a_{4}a4​ for the sequence described. -Geometric, with a5=100a_{5}=100a5​=100 and a7=1a_{7}=1a7​=1

Find the sum, if it exists, of the terms of the infinite geometric sequence. - ∑i=1∞53⋅(−13)i−1\sum_{\mathrm{i}=1}^{\infty} \frac{5}{3} \cdot\left(-\frac{1}{3}\right)^{\mathrm{i}-1}∑i=1∞​35​⋅(−31​)i−1

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - 1,−1,3,−5,…1,-1,3,-5, \ldots1,−1,3,−5,…

Write the series with summation notation. - 7+12+17+22+277+12+17+22+277+12+17+22+27

Find the indicated term for the arithmetic sequence. - a11=−41,a19=−81;a7\mathrm{a}_{11}=-41, \mathrm{a}_{19}=-81 ; \mathrm{a}_{7}a11​=−41,a19​=−81;a7​

Find S5\mathrm{S}_{5}S5​ for the sequence described. -Geometric, with a5=48a_{5}=48a5​=48 and a 7=127=127=12

Find a general term, ana_{n}an​ , for the given terms of the sequence. - 52,54,58,516,532,…\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \frac{5}{16}, \frac{5}{32}, \ldots25​,45​,85​,165​,325​,…

Find the indicated term for the geometric sequence. - a1=4,r=3;a4\mathrm{a}_{1}=4, \mathrm{r}=3 ; \mathrm{a}_{4}a1​=4,r=3;a4​

Find the indicated term for the sequence. - an=n2−na_{n}=n^{2}-nan​=n2−n ; ag

Evaluate the expression - 3!0!3!\frac{3 !}{0 ! 3 !}0!3!3!​

If $1400\$ 1400$1400 is deposited in an ordinary annuity at the end of each quarter for 4yr4 \mathrm{yr}4yr and earns 3%3 \%3% interest compounded quarterly, how much will be in the account at the end of this term?

Find the sum, if it exists, of the terms of the infinite geometric sequence. - ∑i=1∞(3)(−14)i\sum_{\mathrm{i}=1}^{\infty}(3)\left(-\frac{1}{4}\right)^{\mathrm{i}}∑i=1∞​(3)(−41​)i

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

Find the indicated term for the geometric sequence. - a5=−14,a8=132;a15\mathrm{a}_{5}=-\frac{1}{4}, \mathrm{a}_{8}=\frac{1}{32} ; \mathrm{a}_{15}a5​=−41​,a8​=321​;a15​

The population of a town was 27,000 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Find the requested sum for the arithmetic sequence. - an=−5n+8;S5a_{n}=-5 n+8 ; S_{5}an​=−5n+8;S5​

Use the formula for ana_{n}an​ to find the general term for the arithmetic sequence. - a1=4, d=−4\mathrm{a}_{1}=4, \mathrm{~d}=-4a1​=4, d=−4

Write the first five terms of the arithmetic sequence. - a1=7,d=−2a_{1}=7, d=-2a1​=7,d=−2

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 arithmetic mean for the collection of numbers. $11,7,5,14,9,8,17$

Find $a_{4}$ for the sequence described. -Geometric, with $a_{5}=100$ and $a_{7}=1$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\sum_{\mathrm{i}=1}^{\infty} \frac{5}{3} \cdot\left(-\frac{1}{3}\right)^{\mathrm{i}-1}$

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $1,-1,3,-5, \ldots$

Write the series with summation notation. - $7+12+17+22+27$

Find the indicated term for the arithmetic sequence. - $\mathrm{a}_{11}=-41, \mathrm{a}_{19}=-81 ; \mathrm{a}_{7}$

Find $\mathrm{S}_{5}$ for the sequence described. -Geometric, with $a_{5}=48$ and a $7=12$

Find a general term, $a_{n}$ , for the given terms of the sequence. - $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \frac{5}{16}, \frac{5}{32}, \ldots$

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

Find the indicated term for the sequence. - $a_{n}=n^{2}-n$ ; ag

Evaluate the expression - $\frac{3 !}{0 ! 3 !}$

If $\$ 1400$ is deposited in an ordinary annuity at the end of each quarter for $4 \mathrm{yr}$ and earns $3 \%$ interest compounded quarterly, how much will be in the account at the end of this term?

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\sum_{\mathrm{i}=1}^{\infty}(3)\left(-\frac{1}{4}\right)^{\mathrm{i}}$

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

Find the indicated term for the geometric sequence. - $\mathrm{a}_{5}=-\frac{1}{4}, \mathrm{a}_{8}=\frac{1}{32} ; \mathrm{a}_{15}$

Find the requested sum for the arithmetic sequence. - $a_{n}=-5 n+8 ; S_{5}$

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence. - $\mathrm{a}_{1}=4, \mathrm{~d}=-4$

Write the first five terms of the arithmetic sequence. - $a_{1}=7, d=-2$