Question 1

Examine the differences for the sequence, and determine the type of expression
-$1,0,-1,-8,-27$

Accepted Answer

A)  cubic 
B)  linear 
C)  quadratic 
A)  cubic 
B)  linear 
C)  quadratic

Question 2

Find the indicated partial sum for the given sequence
-s10, $1,-73,-147, \ldots$

Accepted Answer

A)  3325 
B)  -3325 
C)  -3320 
D)  3340 
A)  3325 
B)  -3325 
C)  -3320 
D)  3340

Question 3

Find the indicated term for the sequence.
-Find the $12^{\text {th }}$ term of the sequence whose general term is $a_{n}=\frac{2 n-1}{3 n+5}$.

Accepted Answer

A)  $\frac{23}{38}$ 
B)  $\frac{23}{41}$ 
C)  $\frac{21}{41}$ 
D)  $\frac{21}{38}$ 
A)  $\frac{23}{38}$ 
B)  $\frac{23}{41}$ 
C)  $\frac{21}{41}$ 
D)  $\frac{21}{38}$

Question 4

Find the first four terms of the given sequence.
-$\mathrm{a}_{1}=9, \mathrm{a}_{\mathrm{n}}=2 \cdot \mathrm{a}_{\mathrm{n}}-1$

Accepted Answer

A)  $18,36,72,144$ 
B)  $0,4,36,40$ 
C)  $9,36,40,44$ 
D)  $9,18,36,72$ 
A)  $18,36,72,144$ 
B)  $0,4,36,40$ 
C)  $9,36,40,44$ 
D)  $9,18,36,72$

Question 5

Solve the problem.
-To train for a race, Will begins by jogging 12 minutes one day per week. He increases his jogging time by 4 minutes each week. Write the general term of this arithmetic sequence, and find how many weeks it takes for him to reach a jogging time of one hour.

Accepted Answer

A)  $a_{n}=4 n+8 ; 12$ weeks 
B)  $\mathrm{a}_{\mathrm{n}}=4 \mathrm{n}+8$; 13 weeks 
C)  $a_{n}=4 n+12 ; 13$ weeks 
D)  $\mathrm{a}_{\mathrm{n}}=4 \mathrm{n}+12$; 12 weeks 
A)  $a_{n}=4 n+8 ; 12$ weeks 
B)  $\mathrm{a}_{\mathrm{n}}=4 \mathrm{n}+8$; 13 weeks 
C)  $a_{n}=4 n+12 ; 13$ weeks 
D)  $\mathrm{a}_{\mathrm{n}}=4 \mathrm{n}+12$; 12 weeks

Question 6

Solve the problem.
-Suppose you invest $\$ 6569$ at the end of each year into an account earning $5 \%$ interest (compounded annually). At the end of 5 years, how much money will be in the account?

Accepted Answer

A)  $\$ 36,297.87$ 
B)  $\$ 167,677.90$ 
C)  $\$ 35,481.80$ 
D)  $\$ 36,134.30$ 
A)  $\$ 36,297.87$ 
B)  $\$ 167,677.90$ 
C)  $\$ 35,481.80$ 
D)  $\$ 36,134.30$

Question 7

Find the general term $a_n$ of the given sequence
-$4,-1, \frac{1}{4},-\frac{1}{16}, \frac{1}{64}$.

Accepted Answer

A)  $a_{n}=4\left(\frac{1}{4}\right)^{n-1}$ 
B)  $a_{n}=\frac{1}{4}(-4) n-1$ 
C)  $a_{n}=4\left(-\frac{1}{4}\right)^{n-1}$ 
D)  $a_{n}=6\left(-\frac{1}{6}\right)^{n-1}$ 
A)  $a_{n}=4\left(\frac{1}{4}\right)^{n-1}$ 
B)  $a_{n}=\frac{1}{4}(-4) n-1$ 
C)  $a_{n}=4\left(-\frac{1}{4}\right)^{n-1}$ 
D)  $a_{n}=6\left(-\frac{1}{6}\right)^{n-1}$

Question 8

Solve the problem.
-A ball is dropped from a height of 36 feet. On each bounce, it bounces to $87 \%$ of its previous height. How high does it get after the 8th bounce? (Round to the nearest hundredth, if necessary.)

Accepted Answer

A)  13.58 feet 
B)  276.92 feet 
C)  11.82 feet 
D)  186.03 feet 
A)  13.58 feet 
B)  276.92 feet 
C)  11.82 feet 
D)  186.03 feet

Question 9

Evaluate the given binomial coefficient
-${ }_{7} C_{4}$

Accepted Answer

A)  840 
B)  $\frac{7}{12}$ 
C)  35 
D)  105 
A)  840 
B)  $\frac{7}{12}$ 
C)  35 
D)  105

Question 10

Evaluate the given binomial coefficient
-${ }_{13} \mathrm{C}_{8}$

Accepted Answer

A)  1287 
B)  154,440 
C)  $51,891,840$ 
D)  $\frac{13}{40}$ 
A)  1287 
B)  154,440 
C)  $51,891,840$ 
D)  $\frac{13}{40}$

Question 11

Find the common difference,d, of the given arithmetic sequence
-$\frac{1}{2},-\frac{1}{2},-\frac{3}{2},-\frac{5}{2}, \ldots$

Accepted Answer

A)  5 
B)  - 1 
C)  -2 
A)  5 
B)  - 1 
C)  -2

Question 12

Write the sum using summation notation
-$7+12+17+22+27$

Accepted Answer

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

Question 13

Simplify.
-$(3 !)^{2}$

Accepted Answer

A)  4 
B)  36 
C)  9 
D)  12 
A)  4 
B)  36 
C)  9 
D)  12

Question 14

Expand using the binomial theorem
-$(x+3 y)^{3}$

Accepted Answer

A)  $3(x+3 y)$ 
B)  $x^{3}+9 x^{2} y+27 x y^{2}+27 y^{3}$ 
C)  $x^{3}+3 x^{2} y+6 x y+9 x y^{2}+18 y^{2}+27 y^{3}$ 
D)  $x^{3}+27 y^{3}$ 
A)  $3(x+3 y)$ 
B)  $x^{3}+9 x^{2} y+27 x y^{2}+27 y^{3}$ 
C)  $x^{3}+3 x^{2} y+6 x y+9 x y^{2}+18 y^{2}+27 y^{3}$ 
D)  $x^{3}+27 y^{3}$

Examine the differences for the sequence, and determine the type of expression - $1,0,-1,-8,-27$

Find the indicated partial sum for the given sequence -s10, $1,-73,-147, \ldots$

Find the indicated term for the sequence. -Find the $12^{\text {th }}$ term of the sequence whose general term is $a_{n}=\frac{2 n-1}{3 n+5}$ .

Find the first four terms of the given sequence. - $\mathrm{a}_{1}=9, \mathrm{a}_{\mathrm{n}}=2 \cdot \mathrm{a}_{\mathrm{n}}-1$

Solve the problem. -To train for a race, Will begins by jogging 12 minutes one day per week. He increases his jogging time by 4 minutes each week. Write the general term of this arithmetic sequence, and find how many weeks it takes for him to reach a jogging time of one hour.

Solve the problem. -Suppose you invest $\$ 6569$ at the end of each year into an account earning $5 \%$ interest (compounded annually). At the end of 5 years, how much money will be in the account?

Find the general term $a_n$ of the given sequence - $4,-1, \frac{1}{4},-\frac{1}{16}, \frac{1}{64}$ .

Solve the problem. -A ball is dropped from a height of 36 feet. On each bounce, it bounces to $87 \%$ of its previous height. How high does it get after the 8th bounce? (Round to the nearest hundredth, if necessary.)

Evaluate the given binomial coefficient - ${ }_{7} C_{4}$

Evaluate the given binomial coefficient - ${ }_{13} \mathrm{C}_{8}$

Find the common difference,d, of the given arithmetic sequence - $\frac{1}{2},-\frac{1}{2},-\frac{3}{2},-\frac{5}{2}, \ldots$

Write the sum using summation notation - $7+12+17+22+27$

Simplify. - $(3 !)^{2}$

Expand using the binomial theorem - $(x+3 y)^{3}$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Filters

Exam 11: Sequences, Series, and the Binomial Theorem

Examine the differences for the sequence, and determine the type of expression - 1,0,−1,−8,−271,0,-1,-8,-271,0,−1,−8,−27

Find the indicated partial sum for the given sequence -s10, 1,−73,−147,…1,-73,-147, \ldots1,−73,−147,…

Find the indicated term for the sequence. -Find the 12th 12^{\text {th }}12th term of the sequence whose general term is an=2n−13n+5a_{n}=\frac{2 n-1}{3 n+5}an​=3n+52n−1​ .

Find the first four terms of the given sequence. - a1=9,an=2⋅an−1\mathrm{a}_{1}=9, \mathrm{a}_{\mathrm{n}}=2 \cdot \mathrm{a}_{\mathrm{n}}-1a1​=9,an​=2⋅an​−1