Question 1

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$$45,15,5 , \frac { 5 } { 3 } , \ldots$$

Accepted Answer

A)  45 
B)  $\frac { 135 } { 2 }$ 
C)  65 
D)  $- \frac { 45 } { 2 }$ 
A)  45 
B)  $\frac { 135 } { 2 }$ 
C)  65 
D)  $- \frac { 45 } { 2 }$

Question 2

Find the indicated partial sum for the given geometric sequence.
-$\mathrm { s } _ { 6 } , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots$

Accepted Answer

A)  $\frac { 1 } { 64 }$ 
B)  $\frac { 127 } { 128 }$ 
C)  $\frac { 63 } { 64 }$ 
D)  $\frac { 31 } { 384 }$ 
A)  $\frac { 1 } { 64 }$ 
B)  $\frac { 127 } { 128 }$ 
C)  $\frac { 63 } { 64 }$ 
D)  $\frac { 31 } { 384 }$

Question 3

Find the indicated partial sum for the given sequence.
-$55 , - 8 , - 11 , - 14 , - 17 , \ldots$

Accepted Answer

A)  $- 23$ 
B)  $- 70$ 
C)  $- 8$ 
D)  $- 40$ 
A)  $- 23$ 
B)  $- 70$ 
C)  $- 8$ 
D)  $- 40$

Question 4

Evaluate the given binomial coefficient.
-${ } _ { 5 } \mathrm { C } _ { 0 }$

Accepted Answer

A)  4 
B)  1 
C)  0 
D)  5 
A)  4 
B)  1 
C)  0 
D)  5

Question 5

Simplify.
-$( 7 ! ) ^ { 2 }$

Accepted Answer

A)  518,400 
B)  49 
C)  10,080 
D)  $25,401,600$ 
A)  518,400 
B)  49 
C)  10,080 
D)  $25,401,600$

Question 6

Find the common difference,d, of the given arithmetic sequence.
-6, 7, 8, 9, …

Accepted Answer

A)  1 
B)  6 
C)  0.75 
A)  1 
B)  6 
C)  0.75

Question 7

Expand using the binomial theorem.
-$$( x - 2 ) ^ { 4 }$$

Accepted Answer

A)  $x ^ { 4 } - 8 x ^ { 3 } - 16 x ^ { 2 } - 32 x + 16$ 
B)  $x ^ { 4 } - 8 x ^ { 3 } + 24 x ^ { 2 } + 8 x + 16$ 
C)  $x ^ { 4 } - 2 x ^ { 3 } + 24 x ^ { 2 } - 16 x + 16$ 
D)  $x ^ { 4 } - 8 x ^ { 3 } + 24 x ^ { 2 } - 32 x + 16$ 
A)  $x ^ { 4 } - 8 x ^ { 3 } - 16 x ^ { 2 } - 32 x + 16$ 
B)  $x ^ { 4 } - 8 x ^ { 3 } + 24 x ^ { 2 } + 8 x + 16$ 
C)  $x ^ { 4 } - 2 x ^ { 3 } + 24 x ^ { 2 } - 16 x + 16$ 
D)  $x ^ { 4 } - 8 x ^ { 3 } + 24 x ^ { 2 } - 32 x + 16$

Question 8

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 8 years? Round to the nearest unit.

Accepted Answer

A)  1720 
B)  1828 
C)  1993 
D)  2172 
A)  1720 
B)  1828 
C)  1993 
D)  2172

Question 9

Find the common ratio, r, for the geometric sequence.
-3

Accepted Answer

A)  3 
B)  9 
C)  81 
D)  1/ 3 
A)  3 
B)  9 
C)  81 
D)  1/ 3

Question 10

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

Accepted Answer

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

Question 11

Expand using the binomial theorem.
-$$( x + 2 y ) ^ { 6 }$$

Accepted Answer

A)  $x ^ { 6 } + 12 x ^ { 5 } y + 48 x ^ { 4 } y ^ { 2 } + 144 x ^ { 3 } y ^ { 3 } + 192 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
B)  $x ^ { 6 } + 12 x ^ { 5 } y + 64 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 64 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + 2 y ^ { 6 }$ 
C)  $x ^ { 6 } + 12 x ^ { 5 } y + 60 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
D)  $x ^ { 6 } + 12 x ^ { 5 } y + 24 x ^ { 4 } y ^ { 2 } + 36 x ^ { 3 } y ^ { 3 } + 24 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + 2 y ^ { 6 }$ 
A)  $x ^ { 6 } + 12 x ^ { 5 } y + 48 x ^ { 4 } y ^ { 2 } + 144 x ^ { 3 } y ^ { 3 } + 192 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
B)  $x ^ { 6 } + 12 x ^ { 5 } y + 64 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 64 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + 2 y ^ { 6 }$ 
C)  $x ^ { 6 } + 12 x ^ { 5 } y + 60 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
D)  $x ^ { 6 } + 12 x ^ { 5 } y + 24 x ^ { 4 } y ^ { 2 } + 36 x ^ { 3 } y ^ { 3 } + 24 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + 2 y ^ { 6 }$

Question 12

Find the first five terms of the geometric sequence with the given first term and common ratio.
-a1 = 4 $$\mathrm { r }$$

Accepted Answer

A)  4   -12   36   -108   324 
B)  4   1   -6   -5   -8 
C)  -12   36   -108   324   -972 
D)  4   12   36   108   324 
A)  4   -12   36   -108   324 
B)  4   1   -6   -5   -8 
C)  -12   36   -108   324   -972 
D)  4   12   36   108   324

Question 13

Find the first four terms of the given sequence.
-$$a _ { 1 } = 5 , a _ { n } = \left( a _ { n } - 1 \right) ^ { 2 }$$

Accepted Answer

A)  $5,25,125,625$ 
B)  $5,25,625,390,625$ 
C)  $5,4,9,16$ 
D)  $5,10,20,40$ 
A)  $5,25,125,625$ 
B)  $5,25,625,390,625$ 
C)  $5,4,9,16$ 
D)  $5,10,20,40$

Question 14

Simplify.
-$5 ! + 4 !$

Accepted Answer

A)  124 
B)  362,880 
C)  144 
D)  29 
A)  124 
B)  362,880 
C)  144 
D)  29

Question 15

Find the indicated partial sum for the sequence with the given general term.
-s $6 , a _ { n } = 4 n + 1$

Accepted Answer

A)  5 
B)  90 
C)  30 
D)  25 
A)  5 
B)  90 
C)  30 
D)  25

Question 16

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 17

Find the common difference,d, of the given arithmetic sequence.
-5, 8, 11, 14, …

Accepted Answer

A)  -3 
B)  3 
C)  9 
A)  -3 
B)  3 
C)  9

Question 18

Write the sum using summation notation.
-$$0 + 2 + 6 + 12 + 20$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 5 } ( 2 i - 2 )$ 
B)  $\sum_{i=1}^{5}\left(i^{2}+i\right)$ 
C)  $\sum _ { i = 1 } ^ { 5 } \left( i ^ { 2 } + i - 2 \right)$ 
D)  $\sum _ { i = 1 } ^ { 5 } \left( i ^ { 2 } - i \right)$ 
A)  $\sum _ { i = 1 } ^ { 5 } ( 2 i - 2 )$ 
B)  $\sum_{i=1}^{5}\left(i^{2}+i\right)$ 
C)  $\sum _ { i = 1 } ^ { 5 } \left( i ^ { 2 } + i - 2 \right)$ 
D)  $\sum _ { i = 1 } ^ { 5 } \left( i ^ { 2 } - i \right)$

Question 19

Simplify.
-$\frac { 4 ! } { 6 ! }$

Accepted Answer

A)  $\frac { 1 } { 2 ! }$ 
B)  $\frac { 1 } { 30 }$ 
C)  2 ! 
D)  30 
A)  $\frac { 1 } { 2 ! }$ 
B)  $\frac { 1 } { 30 }$ 
C)  2 ! 
D)  30

Question 20

Find the first five terms of the sequence with the given general term.
-$$a _ { n } = 2 n - 3$$

Accepted Answer

A)  $- 1,0,1,2,3$ 
B)  $5,7,9,11,13$ 
C)  $- 1,1,3,5,7$ 
D)  $1 , - 1 , - 3 , - 5 , - 7$ 
A)  $- 1,0,1,2,3$ 
B)  $5,7,9,11,13$ 
C)  $- 1,1,3,5,7$ 
D)  $1 , - 1 , - 3 , - 5 , - 7$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $45,15,5 , \frac { 5 } { 3 } , \ldots$

Find the indicated partial sum for the given geometric sequence. - $\mathrm { s } _ { 6 } , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots$

Find the indicated partial sum for the given sequence. - $55 , - 8 , - 11 , - 14 , - 17 , \ldots$

Evaluate the given binomial coefficient. - ${ } _ { 5 } \mathrm { C } _ { 0 }$

Simplify. - $( 7 ! ) ^ { 2 }$

Find the common difference,d, of the given arithmetic sequence. -6, 7, 8, 9, …

Expand using the binomial theorem. - $( x - 2 ) ^ { 4 }$

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 8 years? Round to the nearest unit.

Find the common ratio, r, for the geometric sequence. -3

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

Expand using the binomial theorem. - $( x + 2 y ) ^ { 6 }$

Find the first five terms of the geometric sequence with the given first term and common ratio. -a1 = 4 $\mathrm { r }$

Find the first four terms of the given sequence. - $a _ { 1 } = 5 , a _ { n } = \left( a _ { n } - 1 \right) ^ { 2 }$

Simplify. - $5 ! + 4 !$

Find the indicated partial sum for the sequence with the given general term. -s $6 , a _ { n } = 4 n + 1$

Simplify. -10!

Find the common difference,d, of the given arithmetic sequence. -5, 8, 11, 14, …

Write the sum using summation notation. - $0 + 2 + 6 + 12 + 20$

Simplify. - $\frac { 4 ! } { 6 ! }$

Find the first five terms of the sequence with the given general term. - $a _ { n } = 2 n - 3$

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

For the given geometric sequence, find the limit of the infinite series, if it exists. - 45,15,5,53,…45,15,5 , \frac { 5 } { 3 } , \ldots45,15,5,35​,…

Find the indicated partial sum for the given geometric sequence. - s6,12,14,18,116,…\mathrm { s } _ { 6 } , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldotss6​,21​,41​,81​,161​,…

Find the indicated partial sum for the given sequence. - 55,−8,−11,−14,−17,…55 , - 8 , - 11 , - 14 , - 17 , \ldots55,−8,−11,−14,−17,…

Evaluate the given binomial coefficient. - 5C0{ } _ { 5 } \mathrm { C } _ { 0 }5​C0​

Simplify. - (7!)2( 7 ! ) ^ { 2 }(7!)2