Question 1

Find the general term, $a_n$, of the given arithmetic sequence
-$\frac{7}{8}, \frac{8}{9}, \frac{9}{10}, \frac{10}{11}, \frac{11}{12}, \ldots$

Accepted Answer

A)  $a_{n}=\frac{n+6}{n-7}$ 
B)  $a_{n}=\frac{6}{n+7}$ 
C)  $a_{n}=\frac{n+6}{n+7}$ 
D)  $a_{n}=\frac{n+7}{n+6}$ 
A)  $a_{n}=\frac{n+6}{n-7}$ 
B)  $a_{n}=\frac{6}{n+7}$ 
C)  $a_{n}=\frac{n+6}{n+7}$ 
D)  $a_{n}=\frac{n+7}{n+6}$

Question 2

Find the general term $a_n$ of the given sequence
-$3,9,27,81,243, \ldots$

Accepted Answer

A)  $a_{n}=3+6(n-1)$ 
B)  $a_{n}=6 n$ 
C)  $a_{n}=3^{n}$ 
D)  $a_{n}=3^{n-1}+2$ 
A)  $a_{n}=3+6(n-1)$ 
B)  $a_{n}=6 n$ 
C)  $a_{n}=3^{n}$ 
D)  $a_{n}=3^{n-1}+2$

Question 3

Find the indicated partial sum for the sequence with the given general term
-$s_{4}, a_{n}=(-1)^{n}$

Accepted Answer

A)  1 
B)  0 
C)  -4 
D)  -1 
A)  1 
B)  0 
C)  -4 
D)  -1

Question 4

Find the indicated partial sum for the given geometric sequence
-$\mathrm{s}_{4}, \frac{1}{27}, \frac{1}{81}, \frac{1}{243}, \frac{1}{729}, \ldots$

Accepted Answer

A)  $\frac{13}{4374}$ 
B)  $\frac{121}{2187}$ 
C)  $\frac{40}{729}$ 
D)  $\frac{1}{729}$ 
A)  $\frac{13}{4374}$ 
B)  $\frac{121}{2187}$ 
C)  $\frac{40}{729}$ 
D)  $\frac{1}{729}$

Question 5

Find the indicated partial sum for the given sequence
-Find the sum of the first 126 odd positive integers.

Accepted Answer

A)  16,129 
B)  16,002 
C)  15,876 
D)  15,625 
A)  16,129 
B)  16,002 
C)  15,876 
D)  15,625

Question 6

The Fibonacci sequence is a sequence whose first two terms are $f_{1}=1$ and $f_{2}=1$, and all other terms are the sum of the two preceding terms. The terms of the Fibonacci sequence are often referred to as Fibonacci numbers.
-The sum of any 10 consecutive Fibonacci numbers is divisible by 11 . Select 10 Fibonacci numbers, and verify this fact.

Accepted Answer

Answers will vary. For 89, 144

Question 7

Simplify.
-$\frac{8 !}{4 ! \cdot 4 !}$

Accepted Answer

A)  35 
B)  70 
C)  1680 
D)  140 
A)  35 
B)  70 
C)  1680 
D)  140

Question 8

Find the first five terms of the sequence with the given general term.
-$a_{n}=n-3$

Accepted Answer

A)  $2,1,0,-1,-2$ 
B)  $-2,-1,0,1,2$ 
C)  $-3,-2,-1,0,1$ 
D)  $2,1,0,1,2$ 
A)  $2,1,0,-1,-2$ 
B)  $-2,-1,0,1,2$ 
C)  $-3,-2,-1,0,1$ 
D)  $2,1,0,1,2$

Question 9

Expand using the binomial theorem
-$(x+3 y)^{6}$

Accepted Answer

A)  $x^{6}+18 x^{5} y+135 x^{4} y^{2}+540 x^{3} y^{3}+1215 x^{2} y^{4}+1458 x y^{5}+729 y^{6}$ 
B)  $x^{6}+18 x^{5} y+36 x^{4} y^{2}+54 x^{3} y^{3}+36 x^{2} y^{4}+18 x y^{5}+3 y^{6}$ 
C)  $x^{6}+18 x^{5} y+108 x^{4} y^{2}+486 x^{3} y^{3}+972 x^{2} y^{4}+1458 x y^{5}+729 y^{6}$ 
D)  $x^{6}+18 x^{5} y+729 x^{4} y^{2}+60 x^{3} y^{3}+729 x^{2} y^{4}+18 x y^{5}+3 y^{6}$ 
A)  $x^{6}+18 x^{5} y+135 x^{4} y^{2}+540 x^{3} y^{3}+1215 x^{2} y^{4}+1458 x y^{5}+729 y^{6}$ 
B)  $x^{6}+18 x^{5} y+36 x^{4} y^{2}+54 x^{3} y^{3}+36 x^{2} y^{4}+18 x y^{5}+3 y^{6}$ 
C)  $x^{6}+18 x^{5} y+108 x^{4} y^{2}+486 x^{3} y^{3}+972 x^{2} y^{4}+1458 x y^{5}+729 y^{6}$ 
D)  $x^{6}+18 x^{5} y+729 x^{4} y^{2}+60 x^{3} y^{3}+729 x^{2} y^{4}+18 x y^{5}+3 y^{6}$

Question 10

Solve.
-One approximation for $\pi$ is the infinite sum $\sum_{i=1}^{\infty}\left[(-1)^{i}+1 \cdot \frac{4}{2 i-1}\right]$. Find the sum of the first 9 terms, rounded to the nearest hundredth.

Accepted Answer

A)  3.22 
B)  3.28 
C)  3.25 
D)  3.24 
A)  3.22 
B)  3.28 
C)  3.25 
D)  3.24

Question 11

Find the sum
-$\sum_{i=1}^{4} \frac{i+1}{i+2}$

Accepted Answer

A)  $\frac{6}{7}$ 
B)  $\frac{61}{20}$ 
C)  $\frac{71}{20}$ 
D)  $\frac{21}{10}$ 
A)  $\frac{6}{7}$ 
B)  $\frac{61}{20}$ 
C)  $\frac{71}{20}$ 
D)  $\frac{21}{10}$

Question 12

Expand using the binomial theorem
-$(4 \mathrm{x}+\mathrm{y})^{3}$

Accepted Answer

A)  $64 x^{3}+32 x^{2} y+8 x y^{2}+y^{3}$ 
B)  $64 x^{3}+48 x^{2}+12 y^{2}+y^{3}$ 
C)  $64 x^{3}+32 x^{2}+8 y^{2}+y^{3}$ 
D)  $64 x^{3}+48 x^{2} y+12 x y^{2}+y^{3}$ 
A)  $64 x^{3}+32 x^{2} y+8 x y^{2}+y^{3}$ 
B)  $64 x^{3}+48 x^{2}+12 y^{2}+y^{3}$ 
C)  $64 x^{3}+32 x^{2}+8 y^{2}+y^{3}$ 
D)  $64 x^{3}+48 x^{2} y+12 x y^{2}+y^{3}$

Question 13

Find the indicated partial sum for the given sequence
-$s_{6}, 2,-2,2,-2, \ldots$

Accepted Answer

A)  2 
B)  4 
C)  -2 
D)  0 
A)  2 
B)  4 
C)  -2 
D)  0

Question 14

Find the indicated partial sum for the given sequence with the given first term and general term
-$\mathrm{s}_{5}, \mathrm{a}_{1}=-1, \mathrm{a}_{\mathrm{n}}=-10 \mathrm{a}_{\mathrm{n}}-1$

Accepted Answer

A)  - 950 
B)  1049 
C)  1050 
D)  - 9091 
A)  - 950 
B)  1049 
C)  1050 
D)  - 9091

Question 15

Solve the problem.
-A man earned $\$ 2500$ the first year he worked. If he received a raise of $\$ 400$ at the end of each year, what was his salary during the 15th year?

Accepted Answer

A)  $\$ 5600$ 
B)  $\$ 8100$ 
C)  $\$ 8500$ 
D)  None of these 
A)  $\$ 5600$ 
B)  $\$ 8100$ 
C)  $\$ 8500$ 
D)  None of these

Question 16

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

Accepted Answer

A)  36 
B)  35 
C)  37 
D)  24 
A)  36 
B)  35 
C)  37 
D)  24

Question 17

Evaluate the given binomial coefficient
-${}_6C_{5}$

Accepted Answer

A)  6 
B)  $\frac{6}{5}$ 
C)  5 
D)  1 
A)  6 
B)  $\frac{6}{5}$ 
C)  5 
D)  1

Question 18

Solve the problem.
-A town has a population of 1000 people and is increasing by $9 \%$ every year. What will the population be at the end of 11 years?

Accepted Answer

A)  2813 
B)  1990 
C)  2367 
D)  2580 
A)  2813 
B)  1990 
C)  2367 
D)  2580

Question 19

Rewrite the given product as a factorial.
-$1 \cdot 2 \cdot 3 \cdots \cdot 19$

Accepted Answer

A)  $18 !$ 
B)  $17 !$ 
C)  20 ! 
D)  19 ! 
A)  $18 !$ 
B)  $17 !$ 
C)  20 ! 
D)  19 !

Question 20

Find the first five terms of the arithmetic sequence with the given first term and common difference
-$\mathrm{a}_{1}=17, \mathrm{~d}=4$

Accepted Answer

A)  $17,4,25,29,33$ 
B)  $4,21,38,55,72$ 
C)  $17,21,25,29,33$ 
D)  $17,4,42,63,84$ 
A)  $17,4,25,29,33$ 
B)  $4,21,38,55,72$ 
C)  $17,21,25,29,33$ 
D)  $17,4,42,63,84$

Find the general term, $a_n$ , of the given arithmetic sequence - $\frac{7}{8}, \frac{8}{9}, \frac{9}{10}, \frac{10}{11}, \frac{11}{12}, \ldots$

Find the general term $a_n$ of the given sequence - $3,9,27,81,243, \ldots$

Find the indicated partial sum for the sequence with the given general term - $s_{4}, a_{n}=(-1)^{n}$

Find the indicated partial sum for the given geometric sequence - $\mathrm{s}_{4}, \frac{1}{27}, \frac{1}{81}, \frac{1}{243}, \frac{1}{729}, \ldots$

Find the indicated partial sum for the given sequence -Find the sum of the first 126 odd positive integers.

Simplify. - $\frac{8 !}{4 ! \cdot 4 !}$

Find the first five terms of the sequence with the given general term. - $a_{n}=n-3$

Expand using the binomial theorem - $(x+3 y)^{6}$

Solve. -One approximation for $\pi$ is the infinite sum $\sum_{i=1}^{\infty}\left[(-1)^{i}+1 \cdot \frac{4}{2 i-1}\right]$ . Find the sum of the first 9 terms, rounded to the nearest hundredth.

Find the sum - $\sum_{i=1}^{4} \frac{i+1}{i+2}$

Expand using the binomial theorem - $(4 \mathrm{x}+\mathrm{y})^{3}$

Find the indicated partial sum for the given sequence - $s_{6}, 2,-2,2,-2, \ldots$

Find the indicated partial sum for the given sequence with the given first term and general term - $\mathrm{s}_{5}, \mathrm{a}_{1}=-1, \mathrm{a}_{\mathrm{n}}=-10 \mathrm{a}_{\mathrm{n}}-1$

Solve the problem. -A man earned $\$ 2500$ the first year he worked. If he received a raise of $\$ 400$ at the end of each year, what was his salary during the 15th year?

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

Evaluate the given binomial coefficient - ${}_6C_{5}$

Solve the problem. -A town has a population of 1000 people and is increasing by $9 \%$ every year. What will the population be at the end of 11 years?

Rewrite the given product as a factorial. - $1 \cdot 2 \cdot 3 \cdots \cdot 19$

Find the first five terms of the arithmetic sequence with the given first term and common difference - $\mathrm{a}_{1}=17, \mathrm{~d}=4$

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

Find the general term, ana_nan​ , of the given arithmetic sequence - 78,89,910,1011,1112,…\frac{7}{8}, \frac{8}{9}, \frac{9}{10}, \frac{10}{11}, \frac{11}{12}, \ldots87​,98​,109​,1110​,1211​,…

Find the general term ana_nan​ of the given sequence - 3,9,27,81,243,…3,9,27,81,243, \ldots3,9,27,81,243,…

Find the indicated partial sum for the sequence with the given general term - s4,an=(−1)ns_{4}, a_{n}=(-1)^{n}s4​,an​=(−1)n

Find the indicated partial sum for the given geometric sequence - s4,127,181,1243,1729,…\mathrm{s}_{4}, \frac{1}{27}, \frac{1}{81}, \frac{1}{243}, \frac{1}{729}, \ldotss4​,271​,811​,2431​,7291​,…

Find the indicated partial sum for the given sequence -Find the sum of the first 126 odd positive integers.

Simplify. - 8!4!⋅4!\frac{8 !}{4 ! \cdot 4 !}4!⋅4!8!​

Find the first five terms of the sequence with the given general term. - an=n−3a_{n}=n-3an​=n−3

Expand using the binomial theorem - (x+3y)6(x+3 y)^{6}(x+3y)6

Solve. -One approximation for π\piπ is the infinite sum ∑i=1∞[(−1)i+1⋅42i−1]\sum_{i=1}^{\infty}\left[(-1)^{i}+1 \cdot \frac{4}{2 i-1}\right]∑i=1∞​[(−1)i+1⋅2i−14​] . Find the sum of the first 9 terms, rounded to the nearest hundredth.

Find the sum - ∑i=14i+1i+2\sum_{i=1}^{4} \frac{i+1}{i+2}∑i=14​i+2i+1​

Expand using the binomial theorem - (4x+y)3(4 \mathrm{x}+\mathrm{y})^{3}(4x+y)3

Find the indicated partial sum for the given sequence - s6,2,−2,2,−2,…s_{6}, 2,-2,2,-2, \ldotss6​,2,−2,2,−2,…

Find the indicated partial sum for the given sequence with the given first term and general term - s5,a1=−1,an=−10an−1\mathrm{s}_{5}, \mathrm{a}_{1}=-1, \mathrm{a}_{\mathrm{n}}=-10 \mathrm{a}_{\mathrm{n}}-1s5​,a1​=−1,an​=−10an​−1

Solve the problem. -A man earned $2500\$ 2500$2500 the first year he worked. If he received a raise of $400\$ 400$400 at the end of each year, what was his salary during the 15th year?

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

Evaluate the given binomial coefficient - 6C5{}_6C_{5}6​C5​

Solve the problem. -A town has a population of 1000 people and is increasing by 9%9 \%9% every year. What will the population be at the end of 11 years?

Rewrite the given product as a factorial. - 1⋅2⋅3⋯⋅191 \cdot 2 \cdot 3 \cdots \cdot 191⋅2⋅3⋯⋅19

Find the first five terms of the arithmetic sequence with the given first term and common difference - a1=17, d=4\mathrm{a}_{1}=17, \mathrm{~d}=4a1​=17, d=4