Question 1

Find the first five terms of the geometric sequence with the given first term and common ratio.
-$$a _ { 1 } = - 4 , r = - \frac { 1 } { 11 }$$

Accepted Answer

A)  $- 4 , \frac { 4 } { 11 } , - \frac { 4 } { 121 } , \frac { 4 } { 1331 } , - \frac { 4 } { 14641 }$ 
B)  $- 4 , - 44 , - 484 , - 5324 , - 58,564$ 
C)  $- 4 , - \frac { 4 } { 11 } , - \frac { 4 } { 121 } , - \frac { 4 } { 1331 } , - \frac { 4 } { 14641 }$ 
D)  $- 4,44 , - 484,5324 , - 58,564$ 
A)  $- 4 , \frac { 4 } { 11 } , - \frac { 4 } { 121 } , \frac { 4 } { 1331 } , - \frac { 4 } { 14641 }$ 
B)  $- 4 , - 44 , - 484 , - 5324 , - 58,564$ 
C)  $- 4 , - \frac { 4 } { 11 } , - \frac { 4 } { 121 } , - \frac { 4 } { 1331 } , - \frac { 4 } { 14641 }$ 
D)  $- 4,44 , - 484,5324 , - 58,564$

Question 2

Find the indicated partial sum for the given sequence.
-Find the sum of the first 187 positive integers.

Accepted Answer

A)  35,156 
B)  17,578 
C)  17,391 
D)  34,969 
A)  35,156 
B)  17,578 
C)  17,391 
D)  34,969

Question 3

Find the partial sum of the geometric sequence with the given first term and common ratio.
-$\mathrm { s } 5 , \mathrm { a } 1 = 1 , \mathrm { r } = \frac { 1 } { 2 }$

Accepted Answer

A)  $- \frac { 1 } { 48 }$ 
B)  $\frac { 1 } { 12 }$ 
C)  93 
D)  $\frac { 31 } { 16 }$ 
A)  $- \frac { 1 } { 48 }$ 
B)  $\frac { 1 } { 12 }$ 
C)  93 
D)  $\frac { 31 } { 16 }$

Question 4

Evaluate the given binomial coefficient.
-${ } _ { 10 } \mathrm { C } _ { 1 }$

Accepted Answer

A)  $\frac { 1 } { 10 }$ 
B)  9 
C)  1 
D)  10 
A)  $\frac { 1 } { 10 }$ 
B)  9 
C)  1 
D)  10

Question 5

Find the indicated partial sum for the given sequence.
-Find the sum of the first 907 even positive integers.

Accepted Answer

A)  823,556 
B)  821,742 
C)  822,649 
D)  824,464 
A)  823,556 
B)  821,742 
C)  822,649 
D)  824,464

Question 6

Solve the problem.
-The number of students in a school in year $n$ is estimated by the model $a _ { n } = 7 n ^ { 2 } + 14 n + 85$. Write a sequence showing how many students are in the school in each of the first three years.

Accepted Answer

A)  $120,155,204$ 
B)  $113,141,190$ 
C)  $106,141,190$ 
D)  $106,141,169$ 
A)  $120,155,204$ 
B)  $113,141,190$ 
C)  $106,141,190$ 
D)  $106,141,169$

Question 7

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$$a _ { n } = 5 \cdot ( 2 ) ^ { n }$$

Accepted Answer

A)  1886 
B)  3072 
C)  No limit 
D)  3441 
A)  1886 
B)  3072 
C)  No limit 
D)  3441

Question 8

Solve the problem.
-$$\text { [ackie is considering a job that offers a monthly starting salary of } \$$$

Accepted Answer

A)  an = 1870 + 130(n - 1) ; $3300 
B)  an = 2000 + 130n ; $3430 
C)  an = 1870 + 130n ; $3430 
D)  an = 2000 + 130n ; $3560 
A)  an = 1870 + 130(n - 1) ; $3300 
B)  an = 2000 + 130n ; $3430 
C)  an = 1870 + 130n ; $3430 
D)  an = 2000 + 130n ; $3560

Question 9

Find the indicated partial sum for the given sequence with the given first term and general term.
-$\mathrm { s } _ { 4 } , \mathrm { a } _ { 1 } = 3 , \mathrm { a } _ { \mathrm { n } } = \left( \mathrm { a } _ { \mathrm { n } } - 1 \right) ^ { 2 } + 1$

Accepted Answer

A)  6655 
B)  10,315 
C)  6657 
D)  10,316 
A)  6655 
B)  10,315 
C)  6657 
D)  10,316

Question 10

Solve the problem.
-The population of a town was 30,700 at the beginning of 1970. If the population decreased 400 people per year, how many people lived in the town at the beginning of 1985?

Accepted Answer

A)  6000 
B)  25,100 
C)  24,300 
D)  24,700 
A)  6000 
B)  25,100 
C)  24,300 
D)  24,700

Question 11

Find the indicated partial sum for the sequence with the given general term.
-s $5 , a _ { n } = 5 n - 11$

Accepted Answer

A)  $- 30$ 
B)  14 
C)  $- 6$ 
D)  20 
A)  $- 30$ 
B)  14 
C)  $- 6$ 
D)  20

Question 12

Find the indicated term for the sequence.
-Find the $6 ^ { \text {th } }$ term of the sequence whose general term is $a _ { n } = ( 5 n - 6 ) ( 2 n + 1 )$.

Accepted Answer

A)  126 
B)  312 
C)  435 
D)  209 
A)  126 
B)  312 
C)  435 
D)  209

Question 13

Find the indicated partial sum for the given sequence.
-s8 $, 3 , - 5,7 , - 9 , \ldots$

Accepted Answer

A)  8 
B)  5 
C)  $- 8$ 
D)  $- 5$ 
A)  8 
B)  5 
C)  $- 8$ 
D)  $- 5$

Question 14

Find the first five terms of the sequence with the given general term.
-$ a_{n}=n^{2}-n $

Accepted Answer

A)  $1,4,9, 16, 25$ 
B)  $2,6,12,20,30$ 
C)  $0,2,6,12,20$ 
D)  $0,3,8,15,24$ 
A)  $1,4,9, 16, 25$ 
B)  $2,6,12,20,30$ 
C)  $0,2,6,12,20$ 
D)  $0,3,8,15,24$

Question 15

Find the indicated term for the sequence.
-Find the $5 ^ { \text {th } }$ term of the sequence whose general term is $a _ { n } = \frac { 2 n - 1 } { 3 n + 4 }$.

Accepted Answer

A)  $\frac { 7 } { 19 }$ 
B)  $\frac { 7 } { 16 }$ 
C)  $\frac { 9 } { 19 }$ 
D)  $\frac { 9 } { 16 }$ 
A)  $\frac { 7 } { 19 }$ 
B)  $\frac { 7 } { 16 }$ 
C)  $\frac { 9 } { 19 }$ 
D)  $\frac { 9 } { 16 }$

Question 16

Find the common difference,d, of the given arithmetic sequence.
-$$- \frac { 3 } { 2 } , - \frac { 7 } { 2 } , - \frac { 11 } { 2 } , - \frac { 15 } { 2 } , \ldots$$

Accepted Answer

A)  5 
B)  $- 4$ 
C)  $- 2$ 
A)  5 
B)  $- 4$ 
C)  $- 2$

Question 17

Find the indicated partial sum for the given sequence with the given first term and general term.
-$\mathrm { s } _ { 4 } , \mathrm { a } _ { 1 } = 4 , \mathrm { a } _ { \mathrm { n } } = 20 \mathrm { a } _ { \mathrm { n } - 1 }$

Accepted Answer

A)  $- 7582$ 
B)  $- 7581$ 
C)  8419 
D)  673,684 
A)  $- 7582$ 
B)  $- 7581$ 
C)  8419 
D)  673,684

Question 18

Find the first four terms of the given sequence.
-$$a _ { 1 } = 6 , a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { a _ { n } - 1 }$$

Accepted Answer

A)  $6 , - \frac { 1 } { 6 } , 6 , - \frac { 1 } { 6 }$ 
B)  $- 6 , \frac { 1 } { 2 } , - \frac { 1 } { 3 } , \frac { 1 } { 4 }$ 
C)  $6 , - \frac { 1 } { 6 } , \frac { 1 } { 36 } , - \frac { 1 } { 216 }$ 
D)  $6 , - \frac { 1 } { 6 } , - 6 , \frac { 1 } { 6 }$ 
A)  $6 , - \frac { 1 } { 6 } , 6 , - \frac { 1 } { 6 }$ 
B)  $- 6 , \frac { 1 } { 2 } , - \frac { 1 } { 3 } , \frac { 1 } { 4 }$ 
C)  $6 , - \frac { 1 } { 6 } , \frac { 1 } { 36 } , - \frac { 1 } { 216 }$ 
D)  $6 , - \frac { 1 } { 6 } , - 6 , \frac { 1 } { 6 }$

Question 19

Find the first five terms of the sequence with the given general term.
-$$a _ { n } = n - 5$$

Accepted Answer

A)  $- 5 , - 4 , - 3 , - 2 , - 1$ 
B)  $- 4 , - 3 , - 2 , - 1,0$ 
C)  $4,3,2,1,0$ 
D)  $4,3 , - 2 , - 1,0$ 
A)  $- 5 , - 4 , - 3 , - 2 , - 1$ 
B)  $- 4 , - 3 , - 2 , - 1,0$ 
C)  $4,3,2,1,0$ 
D)  $4,3 , - 2 , - 1,0$

Question 20

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$5 , \frac { 5 } { 3 } , \frac { 5 } { 9 } , \frac { 5 } { 27 } , \ldots$

Accepted Answer

A)  5 
B)  $\frac { 20 } { 3 }$ 
C)  $\frac { 15 } { 2 }$ 
D)  $\frac { 5 } { 3 }$ 
A)  5 
B)  $\frac { 20 } { 3 }$ 
C)  $\frac { 15 } { 2 }$ 
D)  $\frac { 5 } { 3 }$

Find the first five terms of the geometric sequence with the given first term and common ratio. - $a _ { 1 } = - 4 , r = - \frac { 1 } { 11 }$

Find the indicated partial sum for the given sequence. -Find the sum of the first 187 positive integers.

Find the partial sum of the geometric sequence with the given first term and common ratio. - $\mathrm { s } 5 , \mathrm { a } 1 = 1 , \mathrm { r } = \frac { 1 } { 2 }$

Evaluate the given binomial coefficient. - ${ } _ { 10 } \mathrm { C } _ { 1 }$

Find the indicated partial sum for the given sequence. -Find the sum of the first 907 even positive integers.

Solve the problem. -The number of students in a school in year $n$ is estimated by the model $a _ { n } = 7 n ^ { 2 } + 14 n + 85$ . Write a sequence showing how many students are in the school in each of the first three years.

For the given geometric sequence, find the limit of the infinite series, if it exists. - $a _ { n } = 5 \cdot ( 2 ) ^ { n }$

Solve the problem. - $\text { [ackie is considering a job that offers a monthly starting salary of } \$$

Find the indicated partial sum for the given sequence with the given first term and general term. - $\mathrm { s } _ { 4 } , \mathrm { a } _ { 1 } = 3 , \mathrm { a } _ { \mathrm { n } } = \left( \mathrm { a } _ { \mathrm { n } } - 1 \right) ^ { 2 } + 1$

Solve the problem. -The population of a town was 30,700 at the beginning of 1970. If the population decreased 400 people per year, how many people lived in the town at the beginning of 1985?

Find the indicated partial sum for the sequence with the given general term. -s $5 , a _ { n } = 5 n - 11$

Find the indicated term for the sequence. -Find the $6 ^ { \text {th } }$ term of the sequence whose general term is $a _ { n } = ( 5 n - 6 ) ( 2 n + 1 )$ .

Find the indicated partial sum for the given sequence. -s8 $, 3 , - 5,7 , - 9 , \ldots$

Find the first five terms of the sequence with the given general term. - $a_{n}=n^{2}-n$

Find the indicated term for the sequence. -Find the $5 ^ { \text {th } }$ term of the sequence whose general term is $a _ { n } = \frac { 2 n - 1 } { 3 n + 4 }$ .

Find the common difference,d, of the given arithmetic sequence. - $- \frac { 3 } { 2 } , - \frac { 7 } { 2 } , - \frac { 11 } { 2 } , - \frac { 15 } { 2 } , \ldots$

Find the indicated partial sum for the given sequence with the given first term and general term. - $\mathrm { s } _ { 4 } , \mathrm { a } _ { 1 } = 4 , \mathrm { a } _ { \mathrm { n } } = 20 \mathrm { a } _ { \mathrm { n } - 1 }$

Find the first four terms of the given sequence. - $a _ { 1 } = 6 , a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { a _ { n } - 1 }$

Find the first five terms of the sequence with the given general term. - $a _ { n } = n - 5$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $5 , \frac { 5 } { 3 } , \frac { 5 } { 9 } , \frac { 5 } { 27 } , \ldots$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Filters

Exam 14: Sequences, Series, and the Binomial Theorem

Find the first five terms of the geometric sequence with the given first term and common ratio. - a1=−4,r=−111a _ { 1 } = - 4 , r = - \frac { 1 } { 11 }a1​=−4,r=−111​

Find the indicated partial sum for the given sequence. -Find the sum of the first 187 positive integers.

Find the partial sum of the geometric sequence with the given first term and common ratio. - s5,a1=1,r=12\mathrm { s } 5 , \mathrm { a } 1 = 1 , \mathrm { r } = \frac { 1 } { 2 }s5,a1=1,r=21​

Evaluate the given binomial coefficient. - 10C1{ } _ { 10 } \mathrm { C } _ { 1 }10​C1​