Question 1

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

Accepted Answer

A)  $\frac{45}{8}$ 
B)  $\frac{31}{16}$ 
C)  $\frac{93}{16}$ 
D)  $\frac{45}{16}$ 
A)  $\frac{45}{8}$ 
B)  $\frac{31}{16}$ 
C)  $\frac{93}{16}$ 
D)  $\frac{45}{16}$

Question 2

Use the binomial theorem to expand the expression.
-$(x+y)^{4}$

Accepted Answer

A)  $x^{4}+4 x^{3} y+6 x^{2} y^{2}+4 x y^{3}+y^{4}$ 
B)  $x^{4}+4 x^{2} y^{2}+y^{4}$ 
C)  $x^{4}+4 x^{3} y+4 x^{2} y^{2}+4 x y^{3}+y^{4}$ 
D)  $x^{4}+4 x^{3}+6 x^{2}+4 x+1$ 
A)  $x^{4}+4 x^{3} y+6 x^{2} y^{2}+4 x y^{3}+y^{4}$ 
B)  $x^{4}+4 x^{2} y^{2}+y^{4}$ 
C)  $x^{4}+4 x^{3} y+4 x^{2} y^{2}+4 x y^{3}+y^{4}$ 
D)  $x^{4}+4 x^{3}+6 x^{2}+4 x+1$

Question 3

Find the indicated term of the binomial expansion.
-The middle term of $\left(x^{6}-2 y\right)^{6}$

Accepted Answer

A)  $80 x^{18} y^{3}$ 
B)  $-40 x^{18} y^{6}$ 
C)  $-160 x^{18} y^{3}$ 
D)  $-40 x^{12} y^{3}$ 
A)  $80 x^{18} y^{3}$ 
B)  $-40 x^{18} y^{6}$ 
C)  $-160 x^{18} y^{3}$ 
D)  $-40 x^{12} y^{3}$

Question 4

An investment is worth $\$ 20,000$, and its value is increasing by $10 \%$ every year. What will its value be at the end of 4 years? Round your answer to the nearest dollar.

Accepted Answer

A)  $\$ 29,282$ 
B)  $\$ 9282$ 
C)  $\$ 28,000$ 
D)  $\$ 26,620$ 
A)  $\$ 29,282$ 
B)  $\$ 9282$ 
C)  $\$ 28,000$ 
D)  $\$ 26,620$

Question 5

Can you find the sum of the infinite geometric series $4+12+36+\cdots$ ? Why or Why not?

Accepted Answer

A)  No. This is not a geometric series. 
B)  No. The common ratio, $r$, is greater than 1 . 
C)  Yes. This is a geometric series. 
D)  Yes. The common ratio, $r$, is less than 1 . 
A)  No. This is not a geometric series. 
B)  No. The common ratio, $r$, is greater than 1 . 
C)  Yes. This is a geometric series. 
D)  Yes. The common ratio, $r$, is less than 1 .

Question 6

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence.
-$-14,-10,-6,-2,2$

Accepted Answer

A)  $a_{n}=5 n-19$ 
B)  $\mathrm{a}_{\mathrm{n}}=4 \mathrm{n}-18$ 
C)  $a_{n}=5 n+18$ 
D)  $a_{n}=18 n-4$ 
A)  $a_{n}=5 n-19$ 
B)  $\mathrm{a}_{\mathrm{n}}=4 \mathrm{n}-18$ 
C)  $a_{n}=5 n+18$ 
D)  $a_{n}=18 n-4$

Question 7

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so
-$\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}, \ldots$

Accepted Answer

A)  $\frac{1}{2}$ 
B)  2 
C)  12 
D)  $\frac{1}{12}$ 
A)  $\frac{1}{2}$ 
B)  2 
C)  12 
D)  $\frac{1}{12}$

Question 8

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

Accepted Answer

A)  8 
B)  7 
C)  9 
D)  5 
A)  8 
B)  7 
C)  9 
D)  5

Question 9

Write out the first five terms of the sequence.
-$a_{n}=\frac{(-1)^{n}}{n^{2}-2}$

Accepted Answer

A)  $-\frac{1}{2}, 1, \frac{1}{2},-\frac{1}{7}, \frac{1}{14}$ 
B)  $-1,-\frac{1}{2}, \frac{1}{7},-\frac{1}{14}, \frac{1}{23}$ 
C)  $1, \frac{1}{2},-\frac{1}{7}, \frac{1}{14}, \frac{1}{23}$ 
D)  $1, \frac{1}{2},-\frac{1}{7}, \frac{1}{14},-\frac{1}{23}$ 
A)  $-\frac{1}{2}, 1, \frac{1}{2},-\frac{1}{7}, \frac{1}{14}$ 
B)  $-1,-\frac{1}{2}, \frac{1}{7},-\frac{1}{14}, \frac{1}{23}$ 
C)  $1, \frac{1}{2},-\frac{1}{7}, \frac{1}{14}, \frac{1}{23}$ 
D)  $1, \frac{1}{2},-\frac{1}{7}, \frac{1}{14},-\frac{1}{23}$

Question 10

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so
-$1024,-256,64,-16, \ldots$

Accepted Answer

A)  -4 
B)  $\frac{1}{4}$ 
C)  $-\frac{1}{4}$ 
D)  $-\frac{1}{5}$ 
A)  -4 
B)  $\frac{1}{4}$ 
C)  $-\frac{1}{4}$ 
D)  $-\frac{1}{5}$

Question 11

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

Accepted Answer

A)  1886 
B)  3072 
C)  3441 
D)  Does not exist 
A)  1886 
B)  3072 
C)  3441 
D)  Does not exist

Question 12

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so.
-$4,5,6,7, \ldots$

Accepted Answer

A)  -1 
B)  3 
C)  1 
D)  Not arithmetic 
A)  -1 
B)  3 
C)  1 
D)  Not arithmetic

Question 13

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so.
-$-10,-12,-14,-16, \ldots$

Accepted Answer

A)  -4 
B)  -6 
C)  -2 
D)  Not arithmetic 
A)  -4 
B)  -6 
C)  -2 
D)  Not arithmetic

Question 14

Find the sum if it exists.
-$\sum_{i=1}^{5}(-3 i+4)$

Accepted Answer

A)  -25 
B)  5 
C)  -30 
D)  -11 
A)  -25 
B)  5 
C)  -30 
D)  -11

Question 15

Write the series with summation notation.
-$3+9+15+21+27$

Accepted Answer

A)  $\sum_{i=1}^{5}(6 n-3)$ 
B)  $\sum_{i=1}^{6}(6 i-3)$ 
C)  $\sum_{i=1}^{5}(6 i-3)$ 
D)  $\sum_{\mathrm{i}=0}^{5}(6 \mathrm{i}-3)$ 
A)  $\sum_{i=1}^{5}(6 n-3)$ 
B)  $\sum_{i=1}^{6}(6 i-3)$ 
C)  $\sum_{i=1}^{5}(6 i-3)$ 
D)  $\sum_{\mathrm{i}=0}^{5}(6 \mathrm{i}-3)$

Question 16

Write out the terms of the series.
-$\sum_{\mathrm{i}=1}^{3}(\mathrm{x}+\mathrm{i})$

Accepted Answer

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

Question 17

How do you determine the common difference of an arithmetic sequence? Explain in your own words.

Accepted Answer

Answers may vary. On

Question 18

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so.
-$6.24,9.1,11.96,14.82, \ldots$

Accepted Answer

A)  2.86 
B)  2.145 
C)  8.58 
D)  Not arithmetic 
A)  2.86 
B)  2.145 
C)  8.58 
D)  Not arithmetic

Question 19

A certain ball when dropped from a height rebounds $\frac{7}{10}$ of the original height. How high will the ball rebound after the fifth bounce if it was dropped from a height of 32 feet? Round your answer to the nearest tenth of a foot.

Accepted Answer

A)  $5.4 \mathrm{ft}$ 
B)  $3.4 \mathrm{ft}$ 
C)  $7.7 \mathrm{ft}$ 
D)  $6.7 \mathrm{ft}$ 
A)  $5.4 \mathrm{ft}$ 
B)  $3.4 \mathrm{ft}$ 
C)  $7.7 \mathrm{ft}$ 
D)  $6.7 \mathrm{ft}$

Question 20

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so
-$\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}$

Accepted Answer

A)  $\frac{3}{2}$ 
B)  2 
C)  $\frac{1}{2}$ 
D)  $\frac{1}{4}$ 
A)  $\frac{3}{2}$ 
B)  2 
C)  $\frac{1}{2}$ 
D)  $\frac{1}{4}$

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

Use the binomial theorem to expand the expression. - $(x+y)^{4}$

Find the indicated term of the binomial expansion. -The middle term of $\left(x^{6}-2 y\right)^{6}$

An investment is worth $\$ 20,000$ , and its value is increasing by $10 \%$ every year. What will its value be at the end of 4 years? Round your answer to the nearest dollar.

Can you find the sum of the infinite geometric series $4+12+36+\cdots$ ? Why or Why not?

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence. - $-14,-10,-6,-2,2$

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}, \ldots$

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

Write out the first five terms of the sequence. - $a_{n}=\frac{(-1)^{n}}{n^{2}-2}$

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $1024,-256,64,-16, \ldots$

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

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - $4,5,6,7, \ldots$

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - $-10,-12,-14,-16, \ldots$

Find the sum if it exists. - $\sum_{i=1}^{5}(-3 i+4)$

Write the series with summation notation. - $3+9+15+21+27$

Write out the terms of the series. - $\sum_{\mathrm{i}=1}^{3}(\mathrm{x}+\mathrm{i})$

How do you determine the common difference of an arithmetic sequence? Explain in your own words.

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - $6.24,9.1,11.96,14.82, \ldots$

A certain ball when dropped from a height rebounds $\frac{7}{10}$ of the original height. How high will the ball rebound after the fifth bounce if it was dropped from a height of 32 feet? Round your answer to the nearest tenth of a foot.

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}$

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

Use the formula for Sn\mathbf{S}_{\mathbf{n}}Sn​ to find the sum for the geometric sequence. - 3,32,34,38,3163, \frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \frac{3}{16}3,23​,43​,83​,163​

Use the binomial theorem to expand the expression. - (x+y)4(x+y)^{4}(x+y)4

Find the indicated term of the binomial expansion. -The middle term of (x6−2y)6\left(x^{6}-2 y\right)^{6}(x6−2y)6

An investment is worth $20,000\$ 20,000$20,000 , and its value is increasing by 10%10 \%10% every year. What will its value be at the end of 4 years? Round your answer to the nearest dollar.

Can you find the sum of the infinite geometric series 4+12+36+⋯4+12+36+\cdots4+12+36+⋯ ? Why or Why not?

Use the formula for ana_{n}an​ to find the general term for the arithmetic sequence. - −14,−10,−6,−2,2-14,-10,-6,-2,2−14,−10,−6,−2,2

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - 34,38,316,332,364,…\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}, \ldots43​,83​,163​,323​,643​,…

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

Write out the first five terms of the sequence. - an=(−1)nn2−2a_{n}=\frac{(-1)^{n}}{n^{2}-2}an​=n2−2(−1)n​

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - 1024,−256,64,−16,…1024,-256,64,-16, \ldots1024,−256,64,−16,…

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

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - 4,5,6,7,…4,5,6,7, \ldots4,5,6,7,…

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - −10,−12,−14,−16,…-10,-12,-14,-16, \ldots−10,−12,−14,−16,…

Find the sum if it exists. - ∑i=15(−3i+4)\sum_{i=1}^{5}(-3 i+4)∑i=15​(−3i+4)

Write the series with summation notation. - 3+9+15+21+273+9+15+21+273+9+15+21+27

Write out the terms of the series. - ∑i=13(x+i)\sum_{\mathrm{i}=1}^{3}(\mathrm{x}+\mathrm{i})∑i=13​(x+i)

How do you determine the common difference of an arithmetic sequence? Explain in your own words.

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - 6.24,9.1,11.96,14.82,…6.24,9.1,11.96,14.82, \ldots6.24,9.1,11.96,14.82,…

A certain ball when dropped from a height rebounds 710\frac{7}{10}107​ of the original height. How high will the ball rebound after the fifth bounce if it was dropped from a height of 32 feet? Round your answer to the nearest tenth of a foot.

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - 34,38,316,332,364\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}43​,83​,163​,323​,643​

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

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

Use the binomial theorem to expand the expression. - $(x+y)^{4}$

Find the indicated term of the binomial expansion. -The middle term of $\left(x^{6}-2 y\right)^{6}$

An investment is worth $\$ 20,000$ , and its value is increasing by $10 \%$ every year. What will its value be at the end of 4 years? Round your answer to the nearest dollar.

Can you find the sum of the infinite geometric series $4+12+36+\cdots$ ? Why or Why not?

Use the formula for $a_{n}$ to find the general term for the arithmetic sequence. - $-14,-10,-6,-2,2$

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}, \ldots$

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

Write out the first five terms of the sequence. - $a_{n}=\frac{(-1)^{n}}{n^{2}-2}$

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $1024,-256,64,-16, \ldots$

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

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - $4,5,6,7, \ldots$

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - $-10,-12,-14,-16, \ldots$

Find the sum if it exists. - $\sum_{i=1}^{5}(-3 i+4)$

Write the series with summation notation. - $3+9+15+21+27$

Write out the terms of the series. - $\sum_{\mathrm{i}=1}^{3}(\mathrm{x}+\mathrm{i})$

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - $6.24,9.1,11.96,14.82, \ldots$

A certain ball when dropped from a height rebounds $\frac{7}{10}$ of the original height. How high will the ball rebound after the fifth bounce if it was dropped from a height of 32 feet? Round your answer to the nearest tenth of a foot.

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}$