Question 1

Find the first four terms of the given sequence.
-$$a _ { 1 } = - 2 , a _ { n } = 2 \cdot a _ { n } - 1$$

Accepted Answer

A)  $- 2 , - 4 , - 8 , - 16$ 
B)  $- 2 , - 10 , - 5,0$ 
C)  $- 4 , - 8 , - 16 , - 32$ 
D)  $0,5 , - 10 , - 5$ 
A)  $- 2 , - 4 , - 8 , - 16$ 
B)  $- 2 , - 10 , - 5,0$ 
C)  $- 4 , - 8 , - 16 , - 32$ 
D)  $0,5 , - 10 , - 5$

Question 2

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

Accepted Answer

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

Question 3

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$\frac { 2 } { 3 } \cdot \left( - \frac { 1 } { 3 } \right) ^ { n - 1 }$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  No limit 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 2 } { 3 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  No limit 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 2 } { 3 }$

Question 4

Solve the problem.
-A ball is dropped from a height of 53 feet. On each bounce, it bounces to 72% of its previous height. How high does it get after the 4th bounce? (Round to the nearest hundredth, if necessary.)

Accepted Answer

A)  138.42 feet 
B)  19.78 feet 
C)  14.24 feet 
D)  189.29 feet 
A)  138.42 feet 
B)  19.78 feet 
C)  14.24 feet 
D)  189.29 feet

Question 5

Find the indicated partial sum for the given geometric sequence.
-s8

Accepted Answer

A)  1 
B)  -1 
C)  0 
D)  2 
A)  1 
B)  -1 
C)  0 
D)  2

Question 6

Find the first four terms of the given sequence.
-$$a _ { 1 } = 9 , a _ { n } = a _ { n } - 1 + 3$$

Accepted Answer

A)  $0,3,6,9$ 
B)  $9,3,6,9$ 
C)  $9,12,15,18$ 
D)  $12,15,18,21$ 
A)  $0,3,6,9$ 
B)  $9,3,6,9$ 
C)  $9,12,15,18$ 
D)  $12,15,18,21$

Question 7

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

Accepted Answer

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

Question 8

Find the indicated partial sum for the sequence with the given general term.
-$\mathrm { s } 10 , \mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } }$

Accepted Answer

A)  $- 10$ 
B)  1 
C)  0 
D)  $- 1$ 
A)  $- 10$ 
B)  1 
C)  0 
D)  $- 1$

Question 9

Find the general term, an, of the given geometric sequence.
-$49,7,1 , \ldots$

Accepted Answer

A)  $a _ { n } = 7 ^ { n }$ 
B)  $a _ { n } = 7 ( n - 1 )$ 
C)  $a _ { n } = 7 ^ { n - 1 }$ 
D)  $a _ { n } = 7 ^ { 3 - n }$ 
A)  $a _ { n } = 7 ^ { n }$ 
B)  $a _ { n } = 7 ( n - 1 )$ 
C)  $a _ { n } = 7 ^ { n - 1 }$ 
D)  $a _ { n } = 7 ^ { 3 - n }$

Question 10

Evaluate the given binomial coefficient.
-${ } _ { 12 } \mathrm { C } _ { 11 }$

Accepted Answer

A)  $479,001,600$ 
B)  $\frac { 12 } { 11 }$ 
C)  12 
A)  $479,001,600$ 
B)  $\frac { 12 } { 11 }$ 
C)  12

Question 11

Find the partial sum of the geometric sequence with the given first term and common ratio.
-$9 , a _ { 1 } = \frac { 1 } { 4 } , r = - 3$

Accepted Answer

A)  $\frac { 4915 } { 4 }$ 
B)  $\frac { 4921 } { 4 }$ 
C)  1232 
D)  $\frac { 4919 } { 4 }$ 
A)  $\frac { 4915 } { 4 }$ 
B)  $\frac { 4921 } { 4 }$ 
C)  1232 
D)  $\frac { 4919 } { 4 }$

Question 12

Find the partial sum of the geometric sequence with the given first term and common ratio.
-$\mathrm { s } 13 , \mathrm { a } _ { 1 } = 4 , \mathrm { r } = 3$

Accepted Answer

A)  $3,188,644$ 
B)  $3,188,624$ 
C)  $3,188,646$ 
D)  $3,188,681$ 
A)  $3,188,644$ 
B)  $3,188,624$ 
C)  $3,188,646$ 
D)  $3,188,681$

Question 13

For the given geometric sequence, find the limit of the infinite series, if it exists.
--2, 2, -2, 2, . . .

Accepted Answer

A)  - 2 
B) No limit 
C)  -4 
D) 2 
A)  - 2 
B) No limit 
C)  -4 
D) 2

Question 14

Write the sum using summation notation.
-$$30 + 42 + 54 + 66 + 78$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 6 } ( 12 \mathrm { i } + 18 )$ 
B)  $\sum _ { i = 1 } ^ { 5 } ( 12 n + 18 )$ 
C)  $\sum _ { i = 0 } ^ { 5 } ( 12 i + 18 )$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } ( 12 \mathrm { i } + 18 )$ 
A)  $\sum _ { i = 1 } ^ { 6 } ( 12 \mathrm { i } + 18 )$ 
B)  $\sum _ { i = 1 } ^ { 5 } ( 12 n + 18 )$ 
C)  $\sum _ { i = 0 } ^ { 5 } ( 12 i + 18 )$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } ( 12 \mathrm { i } + 18 )$

Question 15

Find the indicated partial sum for the sequence with the given general term.
-$s 6 , a _ { n } = - 3 n + 6$

Accepted Answer

A)  3 
B)  $- 12$ 
C)  $- 27$ 
D)  18 
A)  3 
B)  $- 12$ 
C)  $- 27$ 
D)  18

Question 16

Find the common ratio, r, for the geometric sequence.
-$\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 } , \ldots$

Accepted Answer

A)  16 
B)  6 
C)  4 
D)  2 
A)  16 
B)  6 
C)  4 
D)  2

Question 17

Simplify.
-$\frac { 8 ! } { 0 ! \cdot 8 ! }$

Accepted Answer

A)  1 
B)  8 
C)  0 
D)  40,320 
A)  1 
B)  8 
C)  0 
D)  40,320

Question 18

Expand using the binomial theorem.
-$$( x - 9 y ) ^ { 5 }$$

Accepted Answer

A)  $x ^ { 5 } - 45 x ^ { 4 } y + 1620 x ^ { 3 } y ^ { 2 } - 14,580 x ^ { 2 } y ^ { 3 } + 32,805 x y ^ { 4 } - 59,049 y ^ { 5 }$ 
B)  $x ^ { 5 } - 45 x ^ { 4 } y + 1620 x ^ { 3 } y ^ { 2 } - 14,580 x ^ { 2 } y ^ { 3 } + 32,805 x y ^ { 4 } - 9 y ^ { 5 }$ 
C)  $x ^ { 5 } - 45 x ^ { 4 } y + 810 x ^ { 3 } y ^ { 2 } - 7290 x ^ { 2 } y ^ { 3 } + 32,805 x y ^ { 4 } - 59,049 y ^ { 5 }$ 
D)  $x ^ { 5 } - 45 x ^ { 4 } y + 810 x ^ { 3 } y ^ { 2 } - 7290 x ^ { 2 } y ^ { 3 } + 32,805 x y ^ { 4 } - 59,049$ 
A)  $x ^ { 5 } - 45 x ^ { 4 } y + 1620 x ^ { 3 } y ^ { 2 } - 14,580 x ^ { 2 } y ^ { 3 } + 32,805 x y ^ { 4 } - 59,049 y ^ { 5 }$ 
B)  $x ^ { 5 } - 45 x ^ { 4 } y + 1620 x ^ { 3 } y ^ { 2 } - 14,580 x ^ { 2 } y ^ { 3 } + 32,805 x y ^ { 4 } - 9 y ^ { 5 }$ 
C)  $x ^ { 5 } - 45 x ^ { 4 } y + 810 x ^ { 3 } y ^ { 2 } - 7290 x ^ { 2 } y ^ { 3 } + 32,805 x y ^ { 4 } - 59,049 y ^ { 5 }$ 
D)  $x ^ { 5 } - 45 x ^ { 4 } y + 810 x ^ { 3 } y ^ { 2 } - 7290 x ^ { 2 } y ^ { 3 } + 32,805 x y ^ { 4 } - 59,049$

Question 19

Write the sum using summation notation.
-$$14 + 19 + 24 + 29 + 34$$

Accepted Answer

A)  $\sum _ { \mathrm { i } = 1 } ^ { 4 } ( 5 \mathrm { i } + 9 )$ 
B)  $\sum _ { i = 1 } ^ { 5 } ( 5 i + 9 )$ 
C)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } 5 \mathrm { i }$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } ( \mathrm { i } + 9 )$ 
A)  $\sum _ { \mathrm { i } = 1 } ^ { 4 } ( 5 \mathrm { i } + 9 )$ 
B)  $\sum _ { i = 1 } ^ { 5 } ( 5 i + 9 )$ 
C)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } 5 \mathrm { i }$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } ( \mathrm { i } + 9 )$

Question 20

Find the indicated partial sum for the given sequence.
-Find the sum of the first 250 odd positive integers.

Accepted Answer

A)  62,750 
B)  62,001 
C)  63,001 
D)  62,500 
A)  62,750 
B)  62,001 
C)  63,001 
D)  62,500

Find the first four terms of the given sequence. - $a _ { 1 } = - 2 , a _ { n } = 2 \cdot a _ { n } - 1$

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

For the given geometric sequence, find the limit of the infinite series, if it exists. - $\frac { 2 } { 3 } \cdot \left( - \frac { 1 } { 3 } \right) ^ { n - 1 }$

Solve the problem. -A ball is dropped from a height of 53 feet. On each bounce, it bounces to 72% of its previous height. How high does it get after the 4th bounce? (Round to the nearest hundredth, if necessary.)

Find the indicated partial sum for the given geometric sequence. -s8

Find the first four terms of the given sequence. - $a _ { 1 } = 9 , a _ { n } = a _ { n } - 1 + 3$

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

Find the indicated partial sum for the sequence with the given general term. - $\mathrm { s } 10 , \mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } }$

Find the general term, an, of the given geometric sequence. - $49,7,1 , \ldots$

Evaluate the given binomial coefficient. - ${ } _ { 12 } \mathrm { C } _ { 11 }$

Find the partial sum of the geometric sequence with the given first term and common ratio. - $9 , a _ { 1 } = \frac { 1 } { 4 } , r = - 3$

Find the partial sum of the geometric sequence with the given first term and common ratio. - $\mathrm { s } 13 , \mathrm { a } _ { 1 } = 4 , \mathrm { r } = 3$

For the given geometric sequence, find the limit of the infinite series, if it exists. --2, 2, -2, 2, . . .

Write the sum using summation notation. - $30 + 42 + 54 + 66 + 78$

Find the indicated partial sum for the sequence with the given general term. - $s 6 , a _ { n } = - 3 n + 6$

Find the common ratio, r, for the geometric sequence. - $\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 } , \ldots$

Simplify. - $\frac { 8 ! } { 0 ! \cdot 8 ! }$

Expand using the binomial theorem. - $( x - 9 y ) ^ { 5 }$

Write the sum using summation notation. - $14 + 19 + 24 + 29 + 34$

Find the indicated partial sum for the given sequence. -Find the sum of the first 250 odd positive integers.

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 four terms of the given sequence. - a1=−2,an=2⋅an−1a _ { 1 } = - 2 , a _ { n } = 2 \cdot a _ { n } - 1a1​=−2,an​=2⋅an​−1

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

For the given geometric sequence, find the limit of the infinite series, if it exists. - 23⋅(−13)n−1\frac { 2 } { 3 } \cdot \left( - \frac { 1 } { 3 } \right) ^ { n - 1 }32​⋅(−31​)n−1