Question 1

Find the first five terms of the sequence with the given general term.
-$$a _ { n } = \frac { 1 } { n ^ { 2 } }$$

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)  $1 , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 }$ 
D)  $\frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \frac { 1 } { 36 }$ 
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)  $1 , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 }$ 
D)  $\frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \frac { 1 } { 36 }$

Question 2

Find the general term, an, of the given geometric sequence.
-$\frac { 1 } { 9 } , \frac { 5 } { 9 } , \frac { 25 } { 9 } , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 9 } + 5 ( n - 1 )$ 
B)  $a _ { n } = \frac { 1 } { 9 } + \frac { 4 } { 9 } ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 9 } \right) ^ { n - 1 } + \frac { 4 } { 9 }$ 
D)  $a _ { n } = \frac { 1 } { 9 } ( 5 ) ^ { n - 1 }$ 
A)  $a _ { n } = \frac { 1 } { 9 } + 5 ( n - 1 )$ 
B)  $a _ { n } = \frac { 1 } { 9 } + \frac { 4 } { 9 } ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 9 } \right) ^ { n - 1 } + \frac { 4 } { 9 }$ 
D)  $a _ { n } = \frac { 1 } { 9 } ( 5 ) ^ { n - 1 }$

Question 3

Find the general term, an, of the given geometric sequence.
-$2 , \frac { 1 } { 4 } , \frac { 1 } { 32 } , \ldots$

Accepted Answer

A)  $a _ { n } = 2 \left( \frac { 1 } { 8 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 2 + \frac { 1 } { 8 } ( n - 1 )$ 
C)  $a _ { n } = 2 ^ { n - 1 } - \frac { 7 } { 4 }$ 
D)  $a _ { n } = 2 - \frac { 7 } { 4 } ( n - 1 )$ 
A)  $a _ { n } = 2 \left( \frac { 1 } { 8 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 2 + \frac { 1 } { 8 } ( n - 1 )$ 
C)  $a _ { n } = 2 ^ { n - 1 } - \frac { 7 } { 4 }$ 
D)  $a _ { n } = 2 - \frac { 7 } { 4 } ( n - 1 )$

Question 4

Find the partial sum of the geometric sequence with the given first term and common ratio.
-s9

Accepted Answer

A)  -2064 
B)  -2042 
C)  -2007 
D)  -2044 
A)  -2064 
B)  -2042 
C)  -2007 
D)  -2044

Question 5

Find the indicated partial sum for the given sequence.
-$\mathrm { s } 5 , - \frac { 1 } { 2 } , \frac { 1 } { 4 } , - \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots$

Accepted Answer

A)  $- \frac { 21 } { 64 }$ 
B)  $- \frac { 15 } { 64 }$ 
C)  $- \frac { 11 } { 32 }$ 
D)  $- \frac { 1 } { 32 }$ 
A)  $- \frac { 21 } { 64 }$ 
B)  $- \frac { 15 } { 64 }$ 
C)  $- \frac { 11 } { 32 }$ 
D)  $- \frac { 1 } { 32 }$

Question 6

Simplify.
-10!

Accepted Answer

A)  362,880 
B)  3,628,800 
C)  121,645,100,408,832,000 
D)  39,916,800 
A)  362,880 
B)  3,628,800 
C)  121,645,100,408,832,000 
D)  39,916,800

Question 7

Find the indicated term for the sequence.
-Find the $6 ^ { \text {th } }$ term of the sequence whose general term is $a _ { n } = 4 ( 2 n - 1 )$.

Accepted Answer

A)  48 
B)  54 
C)  40 
D)  44 
A)  48 
B)  54 
C)  40 
D)  44

Question 8

Solve the problem.
-To train for a race, Will begins by jogging 12 minutes one day per week. He increases his jogging time by 5 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)  an = 5n + 12; 10 weeks 
B)  an = 5n + 7; 10 weeks 
C)  an = 5n + 12; 11 weeks 
D)  an = 5n + 7; 11 weeks 
A)  an = 5n + 12; 10 weeks 
B)  an = 5n + 7; 10 weeks 
C)  an = 5n + 12; 11 weeks 
D)  an = 5n + 7; 11 weeks

Question 9

Solve the problem.
-A town has a population of 2000 people and is increasing by 9% every year. What will the population be at the end of 8 years?

Accepted Answer

A)  3656 
B)  4344 
C)  3440 
D)  3985 
A)  3656 
B)  4344 
C)  3440 
D)  3985

Question 10

Find the sum.
-$$\sum _ { i = 1 } ^ { 4 } \left( i ^ { 2 } - 5 i - 3 \right)$$

Accepted Answer

A)  $- 24$ 
B)  $- 32$ 
C)  13 
D)  0 
A)  $- 24$ 
B)  $- 32$ 
C)  13 
D)  0

Question 11

Find the first five terms of the sequence with the given general term.
-$$a _ { n } = 4 ^ { n }$$

Accepted Answer

A)  $1,16,81,256,625$ 
B)  $1,4,16,64,256$ 
C)  $4,16,64,256,1024$ 
D)  $16,64,256,1024,4096$ 
A)  $1,16,81,256,625$ 
B)  $1,4,16,64,256$ 
C)  $4,16,64,256,1024$ 
D)  $16,64,256,1024,4096$

Question 12

Find the common ratio, r, for the geometric sequence.
-$3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \ldots$

Accepted Answer

A)  4 
B)  $\frac { 1 } { 4 }$ 
C)  10 
D)  $\frac { 1 } { 10 }$ 
A)  4 
B)  $\frac { 1 } { 4 }$ 
C)  10 
D)  $\frac { 1 } { 10 }$

Question 13

Find the first five terms of the sequence with the given general term.
-$$a _ { n } = ( - 1 ) ^ { n - 9 }$$

Accepted Answer

A)  $- 1,1 , - 1,1 , - 1$ 
B)  $1,1,1,1,1$ 
C)  $- 1 , - 1 , - 1 , - 1 , - 1$ 
D)  $1 , - 1,1 , - 1,1$ 
A)  $- 1,1 , - 1,1 , - 1$ 
B)  $1,1,1,1,1$ 
C)  $- 1 , - 1 , - 1 , - 1 , - 1$ 
D)  $1 , - 1,1 , - 1,1$

Question 14

Expand using the binomial theorem.
-$$( x - 1 ) ^ { 6 }$$

Accepted Answer

A)  $x ^ { 6 } - 6 x ^ { 5 } - 30 x ^ { 4 } - 120 x ^ { 3 } - 360 x ^ { 2 } - 720 x + 720$ 
B)  $x ^ { 6 } - 6 x ^ { 5 } + 30 x ^ { 4 } - 120 x ^ { 3 } + 30 x ^ { 2 } - 6 x + 1$ 
C)  $x ^ { 6 } - 6 x ^ { 5 } + 15 x ^ { 4 } - 20 x ^ { 3 } + 15 x ^ { 2 } - 6 x + 1$ 
D)  $x ^ { 6 } - 6 x ^ { 5 } - 15 x ^ { 4 } - 20 x ^ { 3 } - 15 x ^ { 2 } - 6 x - 6$ 
A)  $x ^ { 6 } - 6 x ^ { 5 } - 30 x ^ { 4 } - 120 x ^ { 3 } - 360 x ^ { 2 } - 720 x + 720$ 
B)  $x ^ { 6 } - 6 x ^ { 5 } + 30 x ^ { 4 } - 120 x ^ { 3 } + 30 x ^ { 2 } - 6 x + 1$ 
C)  $x ^ { 6 } - 6 x ^ { 5 } + 15 x ^ { 4 } - 20 x ^ { 3 } + 15 x ^ { 2 } - 6 x + 1$ 
D)  $x ^ { 6 } - 6 x ^ { 5 } - 15 x ^ { 4 } - 20 x ^ { 3 } - 15 x ^ { 2 } - 6 x - 6$

Question 15

Find the sum.
-$\sum _ { \mathrm { i } = 2 } ^ { 5 } 4 ^ { \mathrm { i } }$

Accepted Answer

A)  80 
B)  16,384 
C)  1360 
D)  1024 
A)  80 
B)  16,384 
C)  1360 
D)  1024

Question 16

Expand using the binomial theorem.
-$$( x + 2 y ) ^ { 3 }$$

Accepted Answer

A)  $x ^ { 3 } + 8 y ^ { 3 }$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } y + 4 x y + 4 x y ^ { 2 } + 8 y ^ { 2 } + 8 y ^ { 3 }$ 
C)  $x ^ { 3 } + 6 x ^ { 2 } y + 12 x y ^ { 2 } + 8 y ^ { 3 }$ 
D)  $3 ( x + 2 y )$ 
A)  $x ^ { 3 } + 8 y ^ { 3 }$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } y + 4 x y + 4 x y ^ { 2 } + 8 y ^ { 2 } + 8 y ^ { 3 }$ 
C)  $x ^ { 3 } + 6 x ^ { 2 } y + 12 x y ^ { 2 } + 8 y ^ { 3 }$ 
D)  $3 ( x + 2 y )$

Question 17

Evaluate the given binomial coefficient.
-${ } _ { 5 } C _ { 4 }$

Accepted Answer

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

Question 18

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

Accepted Answer

A)  $x ^ { 4 } - 3 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } - 54 x y ^ { 3 } + 81 y ^ { 4 }$ 
B)  $x ^ { 4 } - 12 x ^ { 3 } y - 54 x ^ { 2 } y ^ { 2 } - 108 x y ^ { 3 } + 81 y ^ { 4 }$ 
C)  $x ^ { 4 } - 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } - 108 x y ^ { 3 } + 81 y ^ { 4 }$ 
D)  $x ^ { 4 } - 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } + 12 x y ^ { 3 } + 81 y ^ { 4 }$ 
A)  $x ^ { 4 } - 3 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } - 54 x y ^ { 3 } + 81 y ^ { 4 }$ 
B)  $x ^ { 4 } - 12 x ^ { 3 } y - 54 x ^ { 2 } y ^ { 2 } - 108 x y ^ { 3 } + 81 y ^ { 4 }$ 
C)  $x ^ { 4 } - 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } - 108 x y ^ { 3 } + 81 y ^ { 4 }$ 
D)  $x ^ { 4 } - 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } + 12 x y ^ { 3 } + 81 y ^ { 4 }$

Question 19

Evaluate the given binomial coefficient.
-$5 \mathrm { C } _ { 5 }$

Accepted Answer

A)  30 
B)  120 
C)  1 
D)  $0.5$ 
A)  30 
B)  120 
C)  1 
D)  $0.5$

Question 20

Find the indicated partial sum for the given sequence with the given first term and general term.
-$s _ { 6 } , a _ { 1 } = 8 , a _ { n } = a _ { n } - 1 - 5$

Accepted Answer

A)  $- 27$ 
B)  $- 49$ 
C)  $- 35$ 
D)  $- 10$ 
A)  $- 27$ 
B)  $- 49$ 
C)  $- 35$ 
D)  $- 10$

Find the first five terms of the sequence with the given general term. - $a _ { n } = \frac { 1 } { n ^ { 2 } }$

Find the general term, an, of the given geometric sequence. - $\frac { 1 } { 9 } , \frac { 5 } { 9 } , \frac { 25 } { 9 } , \ldots$

Find the general term, an, of the given geometric sequence. - $2 , \frac { 1 } { 4 } , \frac { 1 } { 32 } , \ldots$

Find the partial sum of the geometric sequence with the given first term and common ratio. -s9

Find the indicated partial sum for the given sequence. - $\mathrm { s } 5 , - \frac { 1 } { 2 } , \frac { 1 } { 4 } , - \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots$

Simplify. -10!

Find the indicated term for the sequence. -Find the $6 ^ { \text {th } }$ term of the sequence whose general term is $a _ { n } = 4 ( 2 n - 1 )$ .

Solve the problem. -To train for a race, Will begins by jogging 12 minutes one day per week. He increases his jogging time by 5 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. -A town has a population of 2000 people and is increasing by 9% every year. What will the population be at the end of 8 years?

Find the sum. - $\sum _ { i = 1 } ^ { 4 } \left( i ^ { 2 } - 5 i - 3 \right)$

Find the first five terms of the sequence with the given general term. - $a _ { n } = 4 ^ { n }$

Find the common ratio, r, for the geometric sequence. - $3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \ldots$

Find the first five terms of the sequence with the given general term. - $a _ { n } = ( - 1 ) ^ { n - 9 }$

Expand using the binomial theorem. - $( x - 1 ) ^ { 6 }$

Find the sum. - $\sum _ { \mathrm { i } = 2 } ^ { 5 } 4 ^ { \mathrm { i } }$

Expand using the binomial theorem. - $( x + 2 y ) ^ { 3 }$

Evaluate the given binomial coefficient. - ${ } _ { 5 } C _ { 4 }$

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

Evaluate the given binomial coefficient. - $5 \mathrm { C } _ { 5 }$

Find the indicated partial sum for the given sequence with the given first term and general term. - $s _ { 6 } , a _ { 1 } = 8 , a _ { n } = a _ { n } - 1 - 5$

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 sequence with the given general term. - an=1n2a _ { n } = \frac { 1 } { n ^ { 2 } }an​=n21​

Find the general term, an, of the given geometric sequence. - 19,59,259,…\frac { 1 } { 9 } , \frac { 5 } { 9 } , \frac { 25 } { 9 } , \ldots91​,95​,925​,…

Find the general term, an, of the given geometric sequence. - 2,14,132,…2 , \frac { 1 } { 4 } , \frac { 1 } { 32 } , \ldots2,41​,321​,…