Question 1

Find the indicated partial sum for the sequence with the given general term.
-$s _ { 3 } , a _ { n } = ( n + 4 ) ( n - 8 )$

Accepted Answer

A)  $- 106$ 
B)  106 
C)  182 
D)  $- 71$ 
A)  $- 106$ 
B)  106 
C)  182 
D)  $- 71$

Question 2

Find the general term, an, of the given geometric sequence.
-$7,49,343 , \ldots$

Accepted Answer

A)  $a _ { n } = 7 ^ { n - 1 } + 6$ 
B)  $a _ { n } = 7 n + 1 - 42$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 7 \mathrm { n }$ 
D)  $a _ { n } = 7 + 42 ( n - 1 )$ 
A)  $a _ { n } = 7 ^ { n - 1 } + 6$ 
B)  $a _ { n } = 7 n + 1 - 42$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 7 \mathrm { n }$ 
D)  $a _ { n } = 7 + 42 ( n - 1 )$

Question 3

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

Accepted Answer

A)  21 
B)  13 
C)  10 
D)  22 
A)  21 
B)  13 
C)  10 
D)  22

Question 4

Find the partial sum of the geometric sequence with the given first term and common ratio.
-$\mathrm { s } _ { 6 } , \mathrm { a } _ { 1 } = 5 , \mathrm { r } = 2$

Accepted Answer

A)  315 
B)  63 
C)  35 
D)  31,248 
A)  315 
B)  63 
C)  35 
D)  31,248

Question 5

Find the sum.
-$$\sum _ { i = 1 } ^ { 6 } ( 4 i - 2 )$$

Accepted Answer

A)  51 
B)  1129 
C)  50 
D)  72 
A)  51 
B)  1129 
C)  50 
D)  72

Question 6

Find the indicated term for the sequence.
-Find the $3 ^ { \text {rd } }$ term of the sequence whose general term is $a _ { n } = 2 ^ { n }$.

Accepted Answer

A)  4 
B)  9 
C)  8 
D)  6 
A)  4 
B)  9 
C)  8 
D)  6

Question 7

Rewrite the given product as a factorial.
-1 ∙ 2 ∙ 3 ∙ ∙ ∙ ∙ ∙ 30

Accepted Answer

A)  31! 
B)  29! 
C)  30! 
D)  28! 
A)  31! 
B)  29! 
C)  30! 
D)  28!

Question 8

Find the general term, an, of the given geometric sequence.
-$$\frac { 1 } { 8 } , \frac { 1 } { 64 } , \frac { 1 } { 512 } , \ldots$$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 8 ^ { n - 1 } + 7 }$ 
B)  $a _ { n } = \frac { 1 } { 8 ^ { n } }$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 8 ^ { \mathrm { n } - 1 }$ 
D)  $a _ { n } = \frac { 1 } { 8 + 56 ( n - 1 ) }$ 
A)  $a _ { n } = \frac { 1 } { 8 ^ { n - 1 } + 7 }$ 
B)  $a _ { n } = \frac { 1 } { 8 ^ { n } }$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 8 ^ { \mathrm { n } - 1 }$ 
D)  $a _ { n } = \frac { 1 } { 8 + 56 ( n - 1 ) }$

Question 9

Find the general term an of the given sequence.
-$4,10,16,22,28 , \ldots$

Accepted Answer

A)  $a _ { n } = 4 ( 6 ) ^ { n - 1 }$ 
B)  $a _ { n } = 2 ( 3 n - 1 )$ 
C)  $a _ { n } = 6 n - 1$ 
D)  $a _ { n } = 2 n - 6$ 
A)  $a _ { n } = 4 ( 6 ) ^ { n - 1 }$ 
B)  $a _ { n } = 2 ( 3 n - 1 )$ 
C)  $a _ { n } = 6 n - 1$ 
D)  $a _ { n } = 2 n - 6$

Question 10

Expand using the binomial theorem.
-$$( x + 8 ) ^ { 5 }$$

Accepted Answer

A)  $x ^ { 5 } + 40 x ^ { 4 } + 640 x ^ { 3 } + 5120 x ^ { 2 } + 20,480 x + 8$ 
B)  $x ^ { 5 } + 40 x ^ { 4 } + 640 x ^ { 3 } + 5120 x ^ { 2 } + 20,480 x + 32,768$ 
C)  $x ^ { 5 } + 40 x ^ { 4 } + 1280 x ^ { 3 } + 10,240 x ^ { 2 } + 20,480 x + 32,768$ 
D)  $x ^ { 5 } + 40 x ^ { 4 } + 1280 x ^ { 3 } + 10,240 x ^ { 2 } + 20,480 x + 8$ 
A)  $x ^ { 5 } + 40 x ^ { 4 } + 640 x ^ { 3 } + 5120 x ^ { 2 } + 20,480 x + 8$ 
B)  $x ^ { 5 } + 40 x ^ { 4 } + 640 x ^ { 3 } + 5120 x ^ { 2 } + 20,480 x + 32,768$ 
C)  $x ^ { 5 } + 40 x ^ { 4 } + 1280 x ^ { 3 } + 10,240 x ^ { 2 } + 20,480 x + 32,768$ 
D)  $x ^ { 5 } + 40 x ^ { 4 } + 1280 x ^ { 3 } + 10,240 x ^ { 2 } + 20,480 x + 8$

Question 11

Find the indicated partial sum for the given sequence.
-$\mathrm { s } _ { 10 } , - 77 , - 117 , - 157 , - 197 , \ldots$

Accepted Answer

A)  1030 
B)  $- 2185$ 
C)  $- 2570$ 
D)  2185 
A)  1030 
B)  $- 2185$ 
C)  $- 2570$ 
D)  2185

Question 12

Find the common difference,d, of the given arithmetic sequence.
--15, -18, -21, -24, …

Accepted Answer

A)  -6 
B) -9 
C) -3 
A)  -6 
B) -9 
C) -3

Question 13

Find the indicated partial sum for the given sequence.
-s8 $8 , - 2,2 , - 2,2 , \ldots$

Accepted Answer

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

Question 14

Simplify.
-$\frac { 8 ! } { 6 ! }$

Accepted Answer

A)  $\frac { 1 } { 2 ! }$ 
B)  2 ! 
C)  $\frac { 1 } { 56 }$ 
D)  56 
A)  $\frac { 1 } { 2 ! }$ 
B)  2 ! 
C)  $\frac { 1 } { 56 }$ 
D)  56

Question 15

Find the partial sum of the geometric sequence with the given first term and common ratio.
-s6, $a _ { 1 } = - 5 , r = 3$

Accepted Answer

A)  $- 1820$ 
B)  1820 
C)  $- 65$ 
D)  $- 364$ 
A)  $- 1820$ 
B)  1820 
C)  $- 65$ 
D)  $- 364$

Question 16

Find the common ratio, r, for the geometric sequence.
-$32,16,8,4 , \ldots$

Accepted Answer

A)  2 
B)  1 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  2 
B)  1 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 1 } { 2 }$

Question 17

Simplify.
-$\frac { 8 ! } { 5 ! \cdot 3 ! }$

Accepted Answer

A)  56 
B)  40,320 
C)  336 
D)  6720 
A)  56 
B)  40,320 
C)  336 
D)  6720

Question 18

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

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 4 } ( - 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = 4 \left( - \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = 4 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 6 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
A)  $a _ { n } = \frac { 1 } { 4 } ( - 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = 4 \left( - \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = 4 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 6 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$

Question 19

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$$4 , - \frac { 4 } { 3 } , \frac { 4 } { 9 } , - \frac { 4 } { 27 } , \ldots$$

Accepted Answer

A)  3 
B)  $- \frac { 4 } { 3 }$ 
C)  4 
D)  $\frac { 8 } { 3 }$ 
A)  3 
B)  $- \frac { 4 } { 3 }$ 
C)  4 
D)  $\frac { 8 } { 3 }$

Question 20

Find the indicated term for the sequence.
-Find the $8 ^ { \text {th } }$ term of the sequence whose general term is $a _ { n } = 3 n - 1$.

Accepted Answer

A)  23 
B)  24 
C)  16 
D)  25 
A)  23 
B)  24 
C)  16 
D)  25

Find the indicated partial sum for the sequence with the given general term. - $s _ { 3 } , a _ { n } = ( n + 4 ) ( n - 8 )$

Find the general term, an, of the given geometric sequence. - $7,49,343 , \ldots$

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

Find the partial sum of the geometric sequence with the given first term and common ratio. - $\mathrm { s } _ { 6 } , \mathrm { a } _ { 1 } = 5 , \mathrm { r } = 2$

Find the sum. - $\sum _ { i = 1 } ^ { 6 } ( 4 i - 2 )$

Find the indicated term for the sequence. -Find the $3 ^ { \text {rd } }$ term of the sequence whose general term is $a _ { n } = 2 ^ { n }$ .

Rewrite the given product as a factorial. -1 ∙ 2 ∙ 3 ∙ ∙ ∙ ∙ ∙ 30

Find the general term, an, of the given geometric sequence. - $\frac { 1 } { 8 } , \frac { 1 } { 64 } , \frac { 1 } { 512 } , \ldots$

Find the general term an of the given sequence. - $4,10,16,22,28 , \ldots$

Expand using the binomial theorem. - $( x + 8 ) ^ { 5 }$

Find the indicated partial sum for the given sequence. - $\mathrm { s } _ { 10 } , - 77 , - 117 , - 157 , - 197 , \ldots$

Find the common difference,d, of the given arithmetic sequence. --15, -18, -21, -24, …

Find the indicated partial sum for the given sequence. -s8 $8 , - 2,2 , - 2,2 , \ldots$

Simplify. - $\frac { 8 ! } { 6 ! }$

Find the partial sum of the geometric sequence with the given first term and common ratio. -s6, $a _ { 1 } = - 5 , r = 3$

Find the common ratio, r, for the geometric sequence. - $32,16,8,4 , \ldots$

Simplify. - $\frac { 8 ! } { 5 ! \cdot 3 ! }$

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

For the given geometric sequence, find the limit of the infinite series, if it exists. - $4 , - \frac { 4 } { 3 } , \frac { 4 } { 9 } , - \frac { 4 } { 27 } , \ldots$

Find the indicated term for the sequence. -Find the $8 ^ { \text {th } }$ term of the sequence whose general term is $a _ { n } = 3 n - 1$ .

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 indicated partial sum for the sequence with the given general term. - s3,an=(n+4)(n−8)s _ { 3 } , a _ { n } = ( n + 4 ) ( n - 8 )s3​,an​=(n+4)(n−8)

Find the general term, an, of the given geometric sequence. - 7,49,343,…7,49,343 , \ldots7,49,343,…

Find the sum. - ∑i=14(3i−2)\sum _ { i = 1 } ^ { 4 } ( 3 i - 2 )∑i=14​(3i−2)

Find the partial sum of the geometric sequence with the given first term and common ratio. - s6,a1=5,r=2\mathrm { s } _ { 6 } , \mathrm { a } _ { 1 } = 5 , \mathrm { r } = 2s6​,a1​=5,r=2

Find the sum. - ∑i=16(4i−2)\sum _ { i = 1 } ^ { 6 } ( 4 i - 2 )∑i=16​(4i−2)

Find the indicated term for the sequence. -Find the 3rd 3 ^ { \text {rd } }3rd term of the sequence whose general term is an=2na _ { n } = 2 ^ { n }an​=2n .