Question 1

Express the sum using summation notation.
-$$\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } \cdot 2 k$$

Accepted Answer

A)  $- 20$ 
B)  20 
C)  16 
D)  4 
A)  $- 20$ 
B)  20 
C)  16 
D)  4 D

Question 2

Find the sum of the arithmetic sequence.
-1 + 2 + 3 + ... + 707

Accepted Answer

A)  250278 
B)  500,556 
C)  499,849 
D)  249571 
A)  250278 
B)  500,556 
C)  499,849 
D)  249571 A

Question 3

The sequence is defined recursively. Write the first four terms.
-a1 = 5 and an = 4an- 1 - 1 for n ≥ 2

Accepted Answer

A)  5, 21, 85, 341 
B)  5, 20, 80, 320 
C)  5, 19, 75, 299 
D)  5, 19, 79, 319 
A)  5, 21, 85, 341 
B)  5, 20, 80, 320 
C)  5, 19, 75, 299 
D)  5, 19, 79, 319 C

Question 4

The sequence is defined recursively. Write the first four terms.
-a1 = 135 and an+1 = 13 (an) for n ≥ 2

Accepted Answer

The answer of The sequence is defined recursively. Write the...

Question 5

Express the sum using summation notation.
-$\sum _ { k = 1 } ^ { 16 } ( 2 k + 7 )$

Accepted Answer

A)  53 
B)  400 
C)  384 
D)  272 
A)  53 
B)  400 
C)  384 
D)  272

Question 6

Express the sum using summation notation.
-$\sum _ { k = 1 } ^ { 6 } ( - k )$

Accepted Answer

A)  $- 5$ 
B)  $- 30$ 
C)  $- 6$ 
D)  $- 21$ 
A)  $- 5$ 
B)  $- 30$ 
C)  $- 6$ 
D)  $- 21$

Question 7

An arithmetic sequence is given. Find the common difference and write out the first four terms.
-{5n + 9}

Accepted Answer

A)  d = 9; 5, 14, 19, 24 
B)  d = 5; 14, 19, 24, 29 
C)  d = 9; 14, 19, 24, 29 
D)  d = 5; 5, 14, 19, 24 
A)  d = 9; 5, 14, 19, 24 
B)  d = 5; 14, 19, 24, 29 
C)  d = 9; 14, 19, 24, 29 
D)  d = 5; 5, 14, 19, 24

Question 8

Determine whether the sequence is geometric.
-2, 6, 18, 54, 162, ...

Accepted Answer

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

Question 9

Express the sum using summation notation.
-$\frac { 1 } { 4 } + \frac { 2 } { 5 } + \frac { 1 } { 2 } + \cdots + \frac { 14 } { 17 }$

Accepted Answer

A) 
$\sum _ { k = 0 } ^ { 14 } \frac { k } { k + 3 }$ 
B) 
$\sum _ { k = 3 } ^ { 14 } \frac { k } { k + 1 }$ 
C) 
$\sum _ { k = 1 } ^ { 14 } \frac { k } { k + 3 }$ 
D) 
$\sum _ { k = 1 } ^ { n } \frac { k } { k + 3 }$ 
A) 
$\sum _ { k = 0 } ^ { 14 } \frac { k } { k + 3 }$ 
B) 
$\sum _ { k = 3 } ^ { 14 } \frac { k } { k + 1 }$ 
C) 
$\sum _ { k = 1 } ^ { 14 } \frac { k } { k + 3 }$ 
D) 
$\sum _ { k = 1 } ^ { n } \frac { k } { k + 3 }$

Question 10

Evaluate the factorial expression.
-$\frac { 7 ! } { 9 ! }$

Accepted Answer

A)  2 ! 
B)  $\frac { 1 } { 72 }$ 
C)  $\frac { 1 } { 2 ! }$ 
D)  72 
A)  2 ! 
B)  $\frac { 1 } { 72 }$ 
C)  $\frac { 1 } { 2 ! }$ 
D)  72

Question 11

Express the sum using summation notation.
-$\frac { 5 ^ { 14 } } { 7 ^ { 3 } } + \frac { 5 ^ { 13 } } { 7 ^ { 4 } } + \frac { 5 ^ { 12 } } { 7 ^ { 5 } } + \ldots + \frac { 5 ^ { 7 } } { 7 ^ { 10 } }$

Accepted Answer

A)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { 15 - k } } { 7 ^ { 2 + k } }$ 
B)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { - k } } { 7 ^ { 2 + k } }$ 
C)  $\sum _ { k = 1 } ^ { 4 } \frac { 5 ^ { 15 + k } } { 7 ^ { 2 + k } }$ 
D)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { 15 - k } } { 7 ^ { k } }$ 
A)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { 15 - k } } { 7 ^ { 2 + k } }$ 
B)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { - k } } { 7 ^ { 2 + k } }$ 
C)  $\sum _ { k = 1 } ^ { 4 } \frac { 5 ^ { 15 + k } } { 7 ^ { 2 + k } }$ 
D)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { 15 - k } } { 7 ^ { k } }$

Question 12

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

Accepted Answer

A)  277 
B)  $- \frac { 57 } { 10 }$ 
C)  $\frac { 17 } { 10 }$ 
D)  $- \frac { 80 } { 27 }$ 
A)  277 
B)  $- \frac { 57 } { 10 }$ 
C)  $\frac { 17 } { 10 }$ 
D)  $- \frac { 80 } { 27 }$

Question 13

Evaluate the factorial expression.
-$\frac { 8 ! } { 7 ! }$

Accepted Answer

A)  1 
B)  $\frac { 8 } { 7 }$ 
C)  8 
D)  $8 !$ 
A)  1 
B)  $\frac { 8 } { 7 }$ 
C)  8 
D)  $8 !$

Question 14

Determine whether the sequence is arithmetic.
-1, 4, 7, 10, 13, ...

Accepted Answer

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

Question 15

Solve.
-A town has a population of 20,000 people and is increasing by 10% every year. What will the population be at the end of 5 years?

Accepted Answer

A)  30,000 people 
B)  32,210 people 
C)  29,282 people 
D)  12,210 people 
A)  30,000 people 
B)  32,210 people 
C)  29,282 people 
D)  12,210 people

Question 16

Determine whether the sequence is geometric.
-3, 5, 7, 11, 13, ...

Accepted Answer

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

Question 17

Solve.
-The number of students in a school in year n is estimated by the model an = 4n2 + 13n + 80. About how many students are in the school in each of the first three years?

Accepted Answer

A)  101, 122, 155 
B)  110, 135, 168 
C)  97, 122, 143 
D)  97, 122, 155 
A)  101, 122, 155 
B)  110, 135, 168 
C)  97, 122, 143 
D)  97, 122, 155

Question 18

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence.
-7th term is 29; 15th term is -27

Accepted Answer

A)  a1 = 78, d = 7, an = an- 1 + 7 
B)  a1 = 71, d = -7, an = an- 1 - 7 
C)  a1 = 71, d = 7, an = an- 1 + 7 
D)  a1 = 78, d = -7, an = an- 1 - 7 
A)  a1 = 78, d = 7, an = an- 1 + 7 
B)  a1 = 71, d = -7, an = an- 1 - 7 
C)  a1 = 71, d = 7, an = an- 1 + 7 
D)  a1 = 78, d = -7, an = an- 1 - 7

Question 19

Write out the sum. Do not evaluate.
-$\sum _ { k = 1 } ^ { 4 } \left( k ^ { 2 } - 4 k - 3 \right)$

Accepted Answer

A)  $- 6 - 7 - 6 - 3 + \ldots$ 
B)  $- 6 - 7 - 6 - 3$ 
C)  $- 6 + 7 - 6 + 3$ 
D)  $1 - 6 - 7 - 6$ 
A)  $- 6 - 7 - 6 - 3 + \ldots$ 
B)  $- 6 - 7 - 6 - 3$ 
C)  $- 6 + 7 - 6 + 3$ 
D)  $1 - 6 - 7 - 6$

Question 20

Express the sum using summation notation.
-$3 ^ { 2 } + 4 ^ { 2 } + 5 ^ { 2 } + \cdots + 9 ^ { 2 }$

Accepted Answer

A) 
$\sum _ { k = 1 } ^ { 9 } k ^ { 2 }$ 
B) 
$\sum _ { k = 4 } ^ { 9 } ( k - 1 ) ^ { 2 }$ 
C) 
$\sum_{k=3}^{9} k^{2}$ 
D) 
$\sum_{k=3}^{n} k^{2}$ 
A) 
$\sum _ { k = 1 } ^ { 9 } k ^ { 2 }$ 
B) 
$\sum _ { k = 4 } ^ { 9 } ( k - 1 ) ^ { 2 }$ 
C) 
$\sum_{k=3}^{9} k^{2}$ 
D) 
$\sum_{k=3}^{n} k^{2}$

Express the sum using summation notation. - $\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } \cdot 2 k$

Find the sum of the arithmetic sequence. -1 + 2 + 3 + ... + 707

The sequence is defined recursively. Write the first four terms. -a1 = 5 and a_n = 4a_n- 1 - 1 for n ≥ 2

The sequence is defined recursively. Write the first four terms. -a1 = 135 and an+1 = 13 (an) for n ≥ 2

Express the sum using summation notation. - $\sum _ { k = 1 } ^ { 16 } ( 2 k + 7 )$

Express the sum using summation notation. - $\sum _ { k = 1 } ^ { 6 } ( - k )$

An arithmetic sequence is given. Find the common difference and write out the first four terms. -{5n + 9}

Determine whether the sequence is geometric. -2, 6, 18, 54, 162, ...

Express the sum using summation notation. - $\frac { 1 } { 4 } + \frac { 2 } { 5 } + \frac { 1 } { 2 } + \cdots + \frac { 14 } { 17 }$

Evaluate the factorial expression. - $\frac { 7 ! } { 9 ! }$

Express the sum using summation notation. - $\frac { 5 ^ { 14 } } { 7 ^ { 3 } } + \frac { 5 ^ { 13 } } { 7 ^ { 4 } } + \frac { 5 ^ { 12 } } { 7 ^ { 5 } } + \ldots + \frac { 5 ^ { 7 } } { 7 ^ { 10 } }$

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

Evaluate the factorial expression. - $\frac { 8 ! } { 7 ! }$

Determine whether the sequence is arithmetic. -1, 4, 7, 10, 13, ...

Solve. -A town has a population of 20,000 people and is increasing by 10% every year. What will the population be at the end of 5 years?

Determine whether the sequence is geometric. -3, 5, 7, 11, 13, ...

Solve. -The number of students in a school in year n is estimated by the model a_n = 4n2 + 13n + 80. About how many students are in the school in each of the first three years?

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is 29; 15th term is -27

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 4 } \left( k ^ { 2 } - 4 k - 3 \right)$

Express the sum using summation notation. - $3 ^ { 2 } + 4 ^ { 2 } + 5 ^ { 2 } + \cdots + 9 ^ { 2 }$

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Exam 7: Sequences; Induction; the Binomial Theorem

Express the sum using summation notation. - ∑k=14(−1)k⋅2k\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } \cdot 2 k∑k=14​(−1)k⋅2k