Question 1

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so
-$2,6,18,54,162$

Accepted Answer

A)  $\frac{1}{3}$ 
B)  3 
C)  6 
D)  Not geometric 
A)  $\frac{1}{3}$ 
B)  3 
C)  6 
D)  Not geometric

Question 2

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

Accepted Answer

A)  $\frac{4}{3}$ 
B)  $\frac{1}{2}$ 
C)  2 
D)  Does not exist 
A)  $\frac{4}{3}$ 
B)  $\frac{1}{2}$ 
C)  2 
D)  Does not exist

Question 3

An auditorium has 25 rows, with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Accepted Answer

A)  850 
B)  900 
C)  550 
D)  500 
A)  850 
B)  900 
C)  550 
D)  500

Question 4

Find the indicated term for the arithmetic sequence.
-$\mathrm{a}_{40}=\frac{204}{5}, \mathrm{a}_{50}=\frac{254}{5} ; \mathrm{a}_{5}$

Accepted Answer

A)  9 
B)  1 
C)  $\frac{29}{5}$ 
D)  $\frac{34}{5}$ 
A)  9 
B)  1 
C)  $\frac{29}{5}$ 
D)  $\frac{34}{5}$

Question 5

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

Accepted Answer

A)  $\frac{1}{4}, \frac{2}{9}, \frac{3}{16}, \frac{4}{25}, \frac{5}{36}$ 
B)  $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ 
C)  $\frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \frac{1}{36}$ 
D)  $1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}$ 
A)  $\frac{1}{4}, \frac{2}{9}, \frac{3}{16}, \frac{4}{25}, \frac{5}{36}$ 
B)  $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ 
C)  $\frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \frac{1}{36}$ 
D)  $1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}$

Question 6

Find the indicated term for the geometric sequence.
-$3,-9,27, \ldots$; a5

Accepted Answer

A)  81 
B)  2187 
C)  243 
D)  -729 
A)  81 
B)  2187 
C)  243 
D)  -729

Question 7

Write out the terms of the series.
-$\sum_{\mathrm{i}=1}^{4} \frac{-\mathrm{x}^{\mathrm{i}}}{\mathrm{i}^{2}}$

Accepted Answer

A)  $-x-\frac{x^{2}}{4}-\frac{x^{3}}{9}-\frac{x^{4}}{16}$ 
B)  $-x-\frac{x^{2}}{2}-\frac{x^{3}}{3}-\frac{x^{4}}{4}$ 
C)  $-x-4 x^{2}-9 x^{3}-16 x^{4}$ 
D)  $-x+\frac{x^{2}}{4}-\frac{x^{3}}{9}+\frac{x^{4}}{16}$ 
A)  $-x-\frac{x^{2}}{4}-\frac{x^{3}}{9}-\frac{x^{4}}{16}$ 
B)  $-x-\frac{x^{2}}{2}-\frac{x^{3}}{3}-\frac{x^{4}}{4}$ 
C)  $-x-4 x^{2}-9 x^{3}-16 x^{4}$ 
D)  $-x+\frac{x^{2}}{4}-\frac{x^{3}}{9}+\frac{x^{4}}{16}$

Question 8

Find the requested sum for the arithmetic sequence.
-$\mathrm{a}_{1}=1, \mathrm{~d}=-5 ; \mathrm{S}_{6}$

Accepted Answer

A)  6 
B)  -29 
C)  -24 
D)  -69 
A)  6 
B)  -29 
C)  -24 
D)  -69

Question 9

Give an example of an arithmetic sequence with $\mathrm{a}_{5}=16$.

Accepted Answer

An example of an arithmetic se

Question 10

Find the indicated term for the sequence.
-$a_{n}=4 n-1 ; a_{8}$

Accepted Answer

A)  32 
B)  33 
C)  24 
D)  31 
A)  32 
B)  33 
C)  24 
D)  31

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $2,6,18,54,162$

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

An auditorium has 25 rows, with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Find the indicated term for the arithmetic sequence. - $\mathrm{a}_{40}=\frac{204}{5}, \mathrm{a}_{50}=\frac{254}{5} ; \mathrm{a}_{5}$

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

Find the indicated term for the geometric sequence. - $3,-9,27, \ldots$ ; a5

Write out the terms of the series. - $\sum_{\mathrm{i}=1}^{4} \frac{-\mathrm{x}^{\mathrm{i}}}{\mathrm{i}^{2}}$

Find the requested sum for the arithmetic sequence. - $\mathrm{a}_{1}=1, \mathrm{~d}=-5 ; \mathrm{S}_{6}$

Give an example of an arithmetic sequence with $\mathrm{a}_{5}=16$ .

Find the indicated term for the sequence. - $a_{n}=4 n-1 ; a_{8}$

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

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - 2,6,18,54,1622,6,18,54,1622,6,18,54,162

Find the sum, if it exists, of the terms of the infinite geometric sequence. - ∑i=1∞43(13)i−1\sum_{i=1}^{\infty} \frac{4}{3}\left(\frac{1}{3}\right)^{i-1}∑i=1∞​34​(31​)i−1

An auditorium has 25 rows, with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Find the indicated term for the arithmetic sequence. - a40=2045,a50=2545;a5\mathrm{a}_{40}=\frac{204}{5}, \mathrm{a}_{50}=\frac{254}{5} ; \mathrm{a}_{5}a40​=5204​,a50​=5254​;a5​

Write out the first five terms of the sequence. - an=1n2a_{n}=\frac{1}{n^{2}}an​=n21​

Find the indicated term for the geometric sequence. - 3,−9,27,…3,-9,27, \ldots3,−9,27,… ; a5

Write out the terms of the series. - ∑i=14−xii2\sum_{\mathrm{i}=1}^{4} \frac{-\mathrm{x}^{\mathrm{i}}}{\mathrm{i}^{2}}∑i=14​i2−xi​

Find the requested sum for the arithmetic sequence. - a1=1, d=−5;S6\mathrm{a}_{1}=1, \mathrm{~d}=-5 ; \mathrm{S}_{6}a1​=1, d=−5;S6​

Give an example of an arithmetic sequence with a5=16\mathrm{a}_{5}=16a5​=16 .

Find the indicated term for the sequence. - an=4n−1;a8a_{n}=4 n-1 ; a_{8}an​=4n−1;a8​

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

If the sequence is geometric, find the common ratio r. If the sequence is not geometric, say so - $2,6,18,54,162$

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

Find the indicated term for the arithmetic sequence. - $\mathrm{a}_{40}=\frac{204}{5}, \mathrm{a}_{50}=\frac{254}{5} ; \mathrm{a}_{5}$

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

Find the indicated term for the geometric sequence. - $3,-9,27, \ldots$ ; a5

Write out the terms of the series. - $\sum_{\mathrm{i}=1}^{4} \frac{-\mathrm{x}^{\mathrm{i}}}{\mathrm{i}^{2}}$

Find the requested sum for the arithmetic sequence. - $\mathrm{a}_{1}=1, \mathrm{~d}=-5 ; \mathrm{S}_{6}$

Give an example of an arithmetic sequence with $\mathrm{a}_{5}=16$ .

Find the indicated term for the sequence. - $a_{n}=4 n-1 ; a_{8}$