Question 1

Find the sum of the arithmetic sequence.
-1 + 3 + 5 + ... + 711

Accepted Answer

A)  126,025 
B)  126,736 
C)  127,449 
D)  127,092 
A)  126,025 
B)  126,736 
C)  127,449 
D)  127,092

Question 2

Find the sum of the arithmetic sequence.
-{5n - 1}, n = 49

Accepted Answer

A)  5953.5 
B)  6272 
C)  6443.5 
D)  6076 
A)  5953.5 
B)  6272 
C)  6443.5 
D)  6076

Question 3

Determine whether the sequence is geometric.
-4, -12, 36, -108, 324, ...

Accepted Answer

A)  Geometric 
B)  Not geometric 
A)  Geometric 
B)  Not geometric

Question 4

Determine whether the sequence is geometric.
-7, 4, 1, -2, -5, ...

Accepted Answer

A)  Geometric 
B)  Not geometric 
A)  Geometric 
B)  Not geometric

Question 5

Solve the problem.
-Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of $1500
per year. How many years will it be before you've made a total (or aggregate) salary of $1,025,000?

Accepted Answer

The answer of Solve the problem.
-Suppose you just received a...

Question 6

Express the sum using summation notation.
-$\sum _ { k = 3 } ^ { 6 } 9 k$

Accepted Answer

A)  81 
B)  108 
C)  54 
D)  162 
A)  81 
B)  108 
C)  54 
D)  162

Question 7

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

Accepted Answer

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

Question 8

Express the sum using summation notation.
-$2 + 8 + 18 + \ldots + 72$

Accepted Answer

A)  $\sum _ { k = 0 } ^ { 6 } 2 k ^ { 2 }$ 
B)  $\sum _ { k = 1 } ^ { 6 } k ^ { 2 }$ 
C)  $\sum _ { k = 1 } ^ { 6 } 2 ^ { 2 } k$ 
D)  $\sum _ { k = 1 } ^ { 6 } 2 k ^ { 2 }$ 
A)  $\sum _ { k = 0 } ^ { 6 } 2 k ^ { 2 }$ 
B)  $\sum _ { k = 1 } ^ { 6 } k ^ { 2 }$ 
C)  $\sum _ { k = 1 } ^ { 6 } 2 ^ { 2 } k$ 
D)  $\sum _ { k = 1 } ^ { 6 } 2 k ^ { 2 }$

Question 9

Write out the sum. Do not evaluate.
-$\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }$

Accepted Answer

A)  $\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 }$ 
B)  $\frac { 1 } { 3 } + \frac { 2 } { 4 } + \frac { 3 } { 5 } + \frac { 4 } { 6 }$ 
C)  $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 }$ 
D)  $\frac { 6 } { 7 }$ 
A)  $\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 }$ 
B)  $\frac { 1 } { 3 } + \frac { 2 } { 4 } + \frac { 3 } { 5 } + \frac { 4 } { 6 }$ 
C)  $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 }$ 
D)  $\frac { 6 } { 7 }$

Question 10

Express the sum using summation notation.
-$$\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 7 k }$$

Accepted Answer

A)  $\frac { 1 } { 28 }$ 
B)  $\frac { 11 } { 42 }$ 
C)  $\frac { 5 } { 28 }$ 
D)  $\frac { 25 } { 84 }$ 
A)  $\frac { 1 } { 28 }$ 
B)  $\frac { 11 } { 42 }$ 
C)  $\frac { 5 } { 28 }$ 
D)  $\frac { 25 } { 84 }$

Question 11

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-3, 6, 12, 24, 48

Accepted Answer

A)  6 
B)  1/2 
C)  2 
D)  Not geometric 
A)  6 
B)  1/2 
C)  2 
D)  Not geometric

Question 12

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence.
-6th term is -10; 15th term is -46

Accepted Answer

A)  a1 = -10, d = -4, an = an- 1 - 4 
B)  a1 = 10, d = -4, an = an- 1 - 4 
C)  a1 = -30, d = 4, an = an- 1 + 4 
D)  a1 = 10, d = 4, an = an- 1 + 4 
A)  a1 = -10, d = -4, an = an- 1 - 4 
B)  a1 = 10, d = -4, an = an- 1 - 4 
C)  a1 = -30, d = 4, an = an- 1 + 4 
D)  a1 = 10, d = 4, an = an- 1 + 4

Question 13

Write out the sum. Do not evaluate.
-$\sum _ { k = 1 } ^ { n } 7 ^ { k + 1 }$

Accepted Answer

A)  $7 + 7 ^ { 2 } + 7 ^ { 3 } + \ldots + 7 ^ { n + 1 }$ 
B)  $7 + 7 ^ { 2 } + 7 ^ { 3 } + \ldots + 7 ^ { n }$ 
C)  $7 ^ { 2 } + 7 ^ { 3 } + 7 ^ { 4 } + \ldots + 7 ^ { n }$ 
D)  $7 ^ { 2 } + 7 ^ { 3 } + 7 ^ { 4 } + \ldots + 7 ^ { n + 1 }$ 
A)  $7 + 7 ^ { 2 } + 7 ^ { 3 } + \ldots + 7 ^ { n + 1 }$ 
B)  $7 + 7 ^ { 2 } + 7 ^ { 3 } + \ldots + 7 ^ { n }$ 
C)  $7 ^ { 2 } + 7 ^ { 3 } + 7 ^ { 4 } + \ldots + 7 ^ { n }$ 
D)  $7 ^ { 2 } + 7 ^ { 3 } + 7 ^ { 4 } + \ldots + 7 ^ { n + 1 }$

Question 14

Find the sum of the arithmetic sequence.
-2 + 4 + 6 + ... + 678

Accepted Answer

A)  115,260 
B)  114,582 
C)  115,600 
D)  114,921 
A)  115,260 
B)  114,582 
C)  115,600 
D)  114,921

Question 15

Find the sum of the arithmetic sequence.
-(-6) + (-1) + 4 + 9 + ... + 39

Accepted Answer

A)  330 
B)  170 
C)  160 
D)  165 
A)  330 
B)  170 
C)  160 
D)  165

Question 16

Solve the problem.
-The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 23,626, what was its population at the beginning of 1997?

Accepted Answer

A)  330,638 inhabitants 
B)  165,319 inhabitants 
C)  25,726 inhabitants 
D)  25,426 inhabitants 
A)  330,638 inhabitants 
B)  165,319 inhabitants 
C)  25,726 inhabitants 
D)  25,426 inhabitants

Question 17

Determine whether the sequence is geometric.
-3, 1, -1, -3, -5, ...

Accepted Answer

A)  Geometric 
B)  Not geometric 
A)  Geometric 
B)  Not geometric

Question 18

Evaluate the factorial expression.
-$\frac { 5 ! } { 3 ! }$

Accepted Answer

A)  $2 !$ 
B)  20 
C)  5 
D)  $\frac { 5 } { 3 }$ 
A)  $2 !$ 
B)  20 
C)  5 
D)  $\frac { 5 } { 3 }$

Question 19

Express the sum using summation notation.
-$\sum _ { k = 2 } ^ { 4 } k ( k - 7 )$

Accepted Answer

A)  $- 3$ 
B)  $- 40$ 
C)  $- 22$ 
D)  $- 34$ 
A)  $- 3$ 
B)  $- 40$ 
C)  $- 22$ 
D)  $- 34$

Question 20

Find the indicated term of the sequence.
-The twenty-fifth term of the arithmetic sequence 3 , -3 , -9 , ...

Accepted Answer

A)  147 
B)  -141 
C)  -147 
D)  153 
A)  147 
B)  -141 
C)  -147 
D)  153

Find the sum of the arithmetic sequence. -1 + 3 + 5 + ... + 711

Find the sum of the arithmetic sequence. -{5n - 1}, n = 49

Determine whether the sequence is geometric. -4, -12, 36, -108, 324, ...

Determine whether the sequence is geometric. -7, 4, 1, -2, -5, ...

Solve the problem. -Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of $1500 per year. How many years will it be before you've made a total (or aggregate) salary of $1,025,000?

Express the sum using summation notation. - $\sum _ { k = 3 } ^ { 6 } 9 k$

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

Express the sum using summation notation. - $2 + 8 + 18 + \ldots + 72$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }$

Express the sum using summation notation. - $\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 7 k }$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. -3, 6, 12, 24, 48

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -6th term is -10; 15th term is -46

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { n } 7 ^ { k + 1 }$

Find the sum of the arithmetic sequence. -2 + 4 + 6 + ... + 678

Find the sum of the arithmetic sequence. -(-6) + (-1) + 4 + 9 + ... + 39

Solve the problem. -The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 23,626, what was its population at the beginning of 1997?

Determine whether the sequence is geometric. -3, 1, -1, -3, -5, ...

Evaluate the factorial expression. - $\frac { 5 ! } { 3 ! }$

Express the sum using summation notation. - $\sum _ { k = 2 } ^ { 4 } k ( k - 7 )$

Find the indicated term of the sequence. -The twenty-fifth term of the arithmetic sequence 3 , -3 , -9 , ...

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Counting and Probability

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Exam 7: Sequences; Induction; the Binomial Theorem

Find the sum of the arithmetic sequence. -1 + 3 + 5 + ... + 711

Find the sum of the arithmetic sequence. -{5n - 1}, n = 49

Determine whether the sequence is geometric. -4, -12, 36, -108, 324, ...

Determine whether the sequence is geometric. -7, 4, 1, -2, -5, ...

Solve the problem. -Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of $1500 per year. How many years will it be before you've made a total (or aggregate) salary of $1,025,000?

Express the sum using summation notation. - ∑k=369k\sum _ { k = 3 } ^ { 6 } 9 k∑k=36​9k

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - 31,34,316,364,3256\frac { 3 } { 1 } , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 }13​,43​,163​,643​,2563​

Express the sum using summation notation. - 2+8+18+…+722 + 8 + 18 + \ldots + 722+8+18+…+72

Write out the sum. Do not evaluate. - ∑k=15k+1k+2\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }∑k=15​k+2k+1​

Express the sum using summation notation. - ∑k=1417k\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 7 k }∑k=14​7k1​

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. -3, 6, 12, 24, 48

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -6th term is -10; 15th term is -46

Write out the sum. Do not evaluate. - ∑k=1n7k+1\sum _ { k = 1 } ^ { n } 7 ^ { k + 1 }∑k=1n​7k+1

Find the sum of the arithmetic sequence. -2 + 4 + 6 + ... + 678

Find the sum of the arithmetic sequence. -(-6) + (-1) + 4 + 9 + ... + 39

Solve the problem. -The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 23,626, what was its population at the beginning of 1997?

Determine whether the sequence is geometric. -3, 1, -1, -3, -5, ...

Evaluate the factorial expression. - 5!3!\frac { 5 ! } { 3 ! }3!5!​

Express the sum using summation notation. - ∑k=24k(k−7)\sum _ { k = 2 } ^ { 4 } k ( k - 7 )∑k=24​k(k−7)

Find the indicated term of the sequence. -The twenty-fifth term of the arithmetic sequence 3 , -3 , -9 , ...

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Counting and Probability

Filters

Express the sum using summation notation. - $\sum _ { k = 3 } ^ { 6 } 9 k$

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

Express the sum using summation notation. - $2 + 8 + 18 + \ldots + 72$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }$

Express the sum using summation notation. - $\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 7 k }$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { n } 7 ^ { k + 1 }$

Evaluate the factorial expression. - $\frac { 5 ! } { 3 ! }$

Express the sum using summation notation. - $\sum _ { k = 2 } ^ { 4 } k ( k - 7 )$