Question 1

Find the sum of the sequence.
-$$\sum _ { k = 1 } ^ { 4 } 3 ^ { k }$$

Accepted Answer

A)  39 
B)  30 
C)  84 
D)  120 
A)  39 
B)  30 
C)  84 
D)  120

Question 2

Find the sum of the sequence.
-$$\sum _ { k = 2 } ^ { 5 } \frac { - 3 } { k }$$

Accepted Answer

A)  $- \frac { 77 } { 20 }$ 
B)  $- \frac { 45 } { 16 }$ 
C)  $\frac { 447 } { 10 }$ 
D)  $\frac { 17 } { 20 }$ 
A)  $- \frac { 77 } { 20 }$ 
B)  $- \frac { 45 } { 16 }$ 
C)  $\frac { 447 } { 10 }$ 
D)  $\frac { 17 } { 20 }$

Question 3

Find the nth term of the geometric sequence.
-$2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 }$

Accepted Answer

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

Question 4

Find the indicated coefficient or term.
-The coefficient of x in the expansion of $$( 3 x + 4 ) ^ { 5 }$$

Accepted Answer

A)  960 
B)  3,840 
C)  5,120 
D)  2,880 
A)  960 
B)  3,840 
C)  5,120 
D)  2,880

Question 5

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-$$\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1,024 }$$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  4 
C)  40 
D)  $\frac { 1 } { 40 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  4 
C)  40 
D)  $\frac { 1 } { 40 }$

Question 6

Determine whether the sequence is arithmetic.
-2, -3, -8, -13, -18, ...

Accepted Answer

A)  Arithmetic 
B)  Not arithmetic 
A)  Arithmetic 
B)  Not arithmetic

Question 7

Find the sum of the sequence.
-$$\sum _ { k = 3 } ^ { 5 } \left( k ^ { 2 } - 9 \right)$$

Accepted Answer

A)  -15 
B)  23 
C)  10 
D)  -3 
A)  -15 
B)  23 
C)  10 
D)  -3

Question 8

Write out the first five terms of the sequence.
-$$\left\{ n ^ { 2 } - n \right\}$$

Accepted Answer

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

Question 9

Write the first four terms of the sequence whose general term is given.
-$$\left\{ \frac { - 2 ( n + 1 ) ! } { n ! } \right\}$$

Accepted Answer

A)  $- 1,0,1,2$ 
B)  $- 4 , - 3 , - \frac { 4 } { 3 } , - \frac { 5 } { 12 }$ 
C)  $- 4 , - 3 , - \frac { 8 } { 3 } , - \frac { 5 } { 2 }$ 
D)  $- 4 , - 6 , - 8 , - 10$ 
A)  $- 1,0,1,2$ 
B)  $- 4 , - 3 , - \frac { 4 } { 3 } , - \frac { 5 } { 12 }$ 
C)  $- 4 , - 3 , - \frac { 8 } { 3 } , - \frac { 5 } { 2 }$ 
D)  $- 4 , - 6 , - 8 , - 10$

Question 10

An arithmetic sequence is given. Find the common difference and write out the first four terms.
-$$\left\{ \frac { 1 } { 3 } + \frac { n } { 8 } \right\}$$

Accepted Answer

A)  $\mathrm { d } = \frac { 1 } { 3 } ; \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 } , \frac { 5 } { 6 }$ 
B)  $\mathrm { d } = \frac { 1 } { 3 } ; \frac { 1 } { 3 } , \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 }$ 
C)  $\mathrm { d } = \frac { 1 } { 8 } ; \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 } , \frac { 5 } { 6 }$ 
D)  $\mathrm { d } = \frac { 1 } { 8 } ; \frac { 1 } { 3 } , \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 }$ 
A)  $\mathrm { d } = \frac { 1 } { 3 } ; \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 } , \frac { 5 } { 6 }$ 
B)  $\mathrm { d } = \frac { 1 } { 3 } ; \frac { 1 } { 3 } , \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 }$ 
C)  $\mathrm { d } = \frac { 1 } { 8 } ; \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 } , \frac { 5 } { 6 }$ 
D)  $\mathrm { d } = \frac { 1 } { 8 } ; \frac { 1 } { 3 } , \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 }$

Question 11

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
-Find a11 when $\mathrm { a } _ { 1 } = - 5 , \mathrm { r } = - 3$

Accepted Answer

A)  885,735 
B)  -35 
C)  -295,245 
D)  -295,241 
A)  885,735 
B)  -35 
C)  -295,245 
D)  -295,241

Question 12

Write out the sum. Do not evaluate.
-$$\sum _ { k = 1 } ^ { 4 } ( k + 6 )$$

Accepted Answer

A)  10 + 11 + 12 + 13 
B)  7 + 8 + 9 + 10 
C)  7 + 8 + 9 + 10 + ... 
D)  6 + 7 + 8 + 9 
A)  10 + 11 + 12 + 13 
B)  7 + 8 + 9 + 10 
C)  7 + 8 + 9 + 10 + ... 
D)  6 + 7 + 8 + 9

Question 13

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-8 , 20 , 32 , 44 , 56 , ... A) $a _ { n } = 8 ( 12 ) ^ { n - 1 }$

Accepted Answer

B)  $a _ { n } = 4 n - 12$ 
C)  $a _ { n } = 12 n - 1$ 
D)  $a _ { n } = 4 ( 3 n - 1 )$ 
B)  $a _ { n } = 4 n - 12$ 
C)  $a _ { n } = 12 n - 1$ 
D)  $a _ { n } = 4 ( 3 n - 1 )$

Question 14

Find the nth term of the geometric sequence.
-$3 , - \frac { 3 } { 5 } , \frac { 3 } { 25 } , - \frac { 3 } { 125 } , \frac { 3 } { 625 }$

Accepted Answer

A)  $a _ { n } = 3 \cdot \left( - \frac { 1 } { 25 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 3 \cdot \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = 3 \cdot \left( - \frac { 1 } { 5 } \right) ^ { n }$ 
D)  $a _ { n } = 3 \cdot \left( - \frac { 1 } { 5 } \right) ^ { n + 1 }$ 
A)  $a _ { n } = 3 \cdot \left( - \frac { 1 } { 25 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 3 \cdot \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = 3 \cdot \left( - \frac { 1 } { 5 } \right) ^ { n }$ 
D)  $a _ { n } = 3 \cdot \left( - \frac { 1 } { 5 } \right) ^ { n + 1 }$

Question 15

Express the sum using summation notation.
-$$\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$$

Accepted Answer

A)  $\sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } } } { \mathrm { kw } }$ 
B)  $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$ 
C)  $\sum _ { k = 0 } ^ { n } \frac {  k } { k w }$ 
D)  $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } - 1 } } { \mathrm { kw } }$ 
A)  $\sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } } } { \mathrm { kw } }$ 
B)  $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$ 
C)  $\sum _ { k = 0 } ^ { n } \frac {  k } { k w }$ 
D)  $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } - 1 } } { \mathrm { kw } }$

Question 16

Express the sum using summation notation.
-2 + 4 + 6 + ... + 14 A)
$\sum _ { k = 0 } ^ { 7 } 2 k$

Accepted Answer

B)  $\sum _ { k = 1 } ^ { 7 } 2 k$ 
C)  $\sum _ { k = 1 } ^ { 7 } k ^ { 2 }$ 
D) 
$\sum _ { k = 1 } ^ { 7 } 2 k ^ { 2 }$ 
B)  $\sum _ { k = 1 } ^ { 7 } 2 k$ 
C)  $\sum _ { k = 1 } ^ { 7 } k ^ { 2 }$ 
D) 
$\sum _ { k = 1 } ^ { 7 } 2 k ^ { 2 }$

Question 17

Find the sum of the sequence.
-$$\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { \mathrm { k } }$$

Accepted Answer

A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 15 } { 16 }$ 
C)  $- \frac { 1 } { 16 }$ 
D)  $- \frac { 5 } { 16 }$ 
A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 15 } { 16 }$ 
C)  $- \frac { 1 } { 16 }$ 
D)  $- \frac { 5 } { 16 }$

Question 18

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-20 + 10 + 5 + ...

Accepted Answer

A)  Converges; 40 
B)  Converges; 20 
C)  Converges; - 20 
D)  Converges; 35 
A)  Converges; 40 
B)  Converges; 20 
C)  Converges; - 20 
D)  Converges; 35

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 4 } 3 ^ { k }$

Find the sum of the sequence. - $\sum _ { k = 2 } ^ { 5 } \frac { - 3 } { k }$

Find the nth term of the geometric sequence. - $2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 }$

Find the indicated coefficient or term. -The coefficient of x in the expansion of $( 3 x + 4 ) ^ { 5 }$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - $\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1,024 }$

Determine whether the sequence is arithmetic. -2, -3, -8, -13, -18, ...

Find the sum of the sequence. - $\sum _ { k = 3 } ^ { 5 } \left( k ^ { 2 } - 9 \right)$

Write out the first five terms of the sequence. - $\left\{ n ^ { 2 } - n \right\}$

Write the first four terms of the sequence whose general term is given. - $\left\{ \frac { - 2 ( n + 1 ) ! } { n ! } \right\}$

An arithmetic sequence is given. Find the common difference and write out the first four terms. - $\left\{ \frac { 1 } { 3 } + \frac { n } { 8 } \right\}$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a11 when $\mathrm { a } _ { 1 } = - 5 , \mathrm { r } = - 3$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 4 } ( k + 6 )$

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. -8 , 20 , 32 , 44 , 56 , ... A) $a _ { n } = 8 ( 12 ) ^ { n - 1 }$ B) $a _ { n } = 4 n - 12$ C) $a _ { n } = 12 n - 1$ D) $a _ { n } = 4 ( 3 n - 1 )$

Find the nth term of the geometric sequence. - $3 , - \frac { 3 } { 5 } , \frac { 3 } { 25 } , - \frac { 3 } { 125 } , \frac { 3 } { 625 }$

Express the sum using summation notation. - $\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$

Express the sum using summation notation. -2 + 4 + 6 + ... + 14 A) $\sum _ { k = 0 } ^ { 7 } 2 k$ B) $\sum _ { k = 1 } ^ { 7 } 2 k$ C) $\sum _ { k = 1 } ^ { 7 } k ^ { 2 }$ D) $\sum _ { k = 1 } ^ { 7 } 2 k ^ { 2 }$

Find the sum of the sequence. - $\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { \mathrm { k } }$

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. -20 + 10 + 5 + ...

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 11: Sequences; Induction; the Binomial Theorem

Find the sum of the sequence. - ∑k=143k\sum _ { k = 1 } ^ { 4 } 3 ^ { k }∑k=14​3k

Find the sum of the sequence. - ∑k=25−3k\sum _ { k = 2 } ^ { 5 } \frac { - 3 } { k }∑k=25​k−3​

Find the nth term of the geometric sequence. - 2,1,12,14,182,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 }2,1,21​,41​,81​

Find the indicated coefficient or term. -The coefficient of x in the expansion of (3x+4)5( 3 x + 4 ) ^ { 5 }(3x+4)5

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - 34,316,364,3256,31,024\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1,024 }43​,163​,643​,2563​,1,0243​