Question 1

The sequence is defined recursively. Write the first four terms.
-a1 = 1 and an = an- 1 - 3 for n ≥ 2

Accepted Answer

A)  -3, -6, -9, -12 
B)  1, -2, -5, -8 
C)  1, 4 , 7 , 10 
D)  1, 0 , -3 , -6 
A)  -3, -6, -9, -12 
B)  1, -2, -5, -8 
C)  1, 4 , 7 , 10 
D)  1, 0 , -3 , -6

Question 2

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

Accepted Answer

A)  14 
B)  30 
C)  20 
D)  18 
A)  14 
B)  30 
C)  20 
D)  18

Question 3

Find the indicated term using the given information.
-a 13 = 80 , a16 = 98 ; a7

Accepted Answer

A)  6 
B)  50 
C)  44 
D)  8 
A)  6 
B)  50 
C)  44 
D)  8

Question 4

Express the sum using summation notation.
-$\sum _ { k = 1 } ^ { 5 } ( k - 10 )$

Accepted Answer

A)  $- 35$ 
B)  $- 30$ 
C)  $- 14$ 
D)  $- 5$ 
A)  $- 35$ 
B)  $- 30$ 
C)  $- 14$ 
D)  $- 5$

Question 5

Find the sum of the arithmetic sequence.
-{3n + 7}, n = 48

Accepted Answer

A)  3864 
B)  4032 
C)  4200 
D)  3792 
A)  3864 
B)  4032 
C)  4200 
D)  3792

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

Determine whether the sequence is arithmetic.
-2, -1, -4, -7, -10, ...

Accepted Answer

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

Question 8

An arithmetic sequence is given. Find the common difference and write out the first four terms.
-{12 - 6n}

Accepted Answer

A)  d = -6; -6, -12, -18, -24 
B)  d = -6; 6, 2 , -4 , -10 
C)  d = -6; 6, 0, -6, -12 
D)  d = 6; 6, 12 , 18 , 24 
A)  d = -6; -6, -12, -18, -24 
B)  d = -6; 6, 2 , -4 , -10 
C)  d = -6; 6, 0, -6, -12 
D)  d = 6; 6, 12 , 18 , 24

Question 9

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence.
-7th term is -2; 15th term is -18

Accepted Answer

A)  a1 = 12, d = -2, an = an- 1 - 2 
B)  a1 = 12, d = 2, an = an- 1 + 2 
C)  a1 = 10, d = 2, an = an- 1 + 2 
D)  a1 = 10, d = -2, an = an- 1 - 2 
A)  a1 = 12, d = -2, an = an- 1 - 2 
B)  a1 = 12, d = 2, an = an- 1 + 2 
C)  a1 = 10, d = 2, an = an- 1 + 2 
D)  a1 = 10, d = -2, an = an- 1 - 2

Question 10

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If
geometric, find the common ratio.
-$$\left\{ \left( \frac { 6 } { 5 } \right) ^ { n } \right\}$$

Accepted Answer

A)  Neither 
B)  Arithmetic, $\mathrm { d } = \frac { 6 } { 5 }$ 
C)  Geometric, $r = \frac { 5 } { 6 }$ 
D)  Geometric, $r = \frac { 6 } { 5 }$ 
A)  Neither 
B)  Arithmetic, $\mathrm { d } = \frac { 6 } { 5 }$ 
C)  Geometric, $r = \frac { 5 } { 6 }$ 
D)  Geometric, $r = \frac { 6 } { 5 }$

Question 11

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

Accepted Answer

A)  $= \frac { 47 } { 256 }$ 
B)  $- \frac { 51 } { 256 }$ 
C)  $\frac { 51 } { 256 }$ 
D)  $\frac { 85 } { 256 }$ 
A)  $= \frac { 47 } { 256 }$ 
B)  $- \frac { 51 } { 256 }$ 
C)  $\frac { 51 } { 256 }$ 
D)  $\frac { 85 } { 256 }$

Question 12

A geometric sequence is given. Find the common ratio and write out the first four terms.
-$$\left\{ 4 \left( \frac { 1 } { 2 } \right) ^ { n - 1 } \right\}$$

Accepted Answer

A)  $a _ { n } = 4 \cdot ( 2 ) ^ { n - 1 }$
$r = 2 ; 4,8,16,32 , \ldots$ 
B)  $a _ { n } = \frac { 1 } { 2 } ( 4 ) ^ { n - 1 }$
$$\mathrm { r } = \frac { 1 } { 2 } ; 4,8,16,32 , \ldots$$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 4 \left( \frac { 1 } { 2 } \right) ^ { \mathrm { n } - 1 }$
$\mathrm { r } = \frac { 1 } { 2 } ; 4,2,1 , \frac { 1 } { 2 } , \ldots$ 
D)  $\mathrm { a } _ { \mathrm { n } } = 4 \left( \frac { 1 } { 4 } \right) ^ { \mathrm { n } - 1 }$
$r = \frac { 1 } { 4 } ; 4,1 , \frac { 1 } { 4 } , \frac { 1 } { 16 } , \ldots$ 
A)  $a _ { n } = 4 \cdot ( 2 ) ^ { n - 1 }$
$r = 2 ; 4,8,16,32 , \ldots$ 
B)  $a _ { n } = \frac { 1 } { 2 } ( 4 ) ^ { n - 1 }$
$$\mathrm { r } = \frac { 1 } { 2 } ; 4,8,16,32 , \ldots$$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 4 \left( \frac { 1 } { 2 } \right) ^ { \mathrm { n } - 1 }$
$\mathrm { r } = \frac { 1 } { 2 } ; 4,2,1 , \frac { 1 } { 2 } , \ldots$ 
D)  $\mathrm { a } _ { \mathrm { n } } = 4 \left( \frac { 1 } { 4 } \right) ^ { \mathrm { n } - 1 }$
$r = \frac { 1 } { 4 } ; 4,1 , \frac { 1 } { 4 } , \frac { 1 } { 16 } , \ldots$

Question 13

Find the indicated term of the sequence.
-The twentieth term of the arithmetic sequence -13, 23, 53, ...

Accepted Answer

A)  -613 
B)  593 
C)  563 
D)  -583 
A)  -613 
B)  593 
C)  563 
D)  -583

Question 14

Write out the first five terms of the sequence.
-During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth year are $ 224,000, then what are the profits for each of the first four years?

Accepted Answer

A)  $14,000, $28,000, $42,000, $56,000 
B)  $14,000, $28,000, $56,000, $140,000 
C)  $14,000, $28,000, $56,000, $112,000 
D)  $15,000, $30,000, $60,000, $118,000 
A)  $14,000, $28,000, $42,000, $56,000 
B)  $14,000, $28,000, $56,000, $140,000 
C)  $14,000, $28,000, $56,000, $112,000 
D)  $15,000, $30,000, $60,000, $118,000

Question 15

Solve the problem.
-A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?

Accepted Answer

A)  1010 seats 
B)  790 seats 
C)  1070 seats 
D)  1092 seats 
A)  1010 seats 
B)  790 seats 
C)  1070 seats 
D)  1092 seats

Question 16

Determine whether the sequence is arithmetic.
-2, 4, 6, 10, 12, ...

Accepted Answer

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

Question 17

Find the sum of the arithmetic sequence.
-6 + 12 + 18 + ... + 492

Accepted Answer

A)  20172 
B)  19926 
C)  20418 
D)  20667 
A)  20172 
B)  19926 
C)  20418 
D)  20667

Question 18

Write out the first five terms of the sequence.
-{2(4n - 3)}

Accepted Answer

A)  2, 4, 6, 8, 10 
B)  1, 5, 9, 13, 17 
C)  -6, 2, 10, 18, 26 
D)  2, 10, 18, 26, 34 
A)  2, 4, 6, 8, 10 
B)  1, 5, 9, 13, 17 
C)  -6, 2, 10, 18, 26 
D)  2, 10, 18, 26, 34

Question 19

Write out the first five terms of the sequence.
-{3n - 1}

Accepted Answer

A)  2, 5, 8, 11, 14 
B)  4, 7, 10, 13, 16 
C)  -2, -5, -8, -11, -14 
D)  2, 3, 4, 5, 6 
A)  2, 5, 8, 11, 14 
B)  4, 7, 10, 13, 16 
C)  -2, -5, -8, -11, -14 
D)  2, 3, 4, 5, 6

Question 20

Express the sum using summation notation.
-$\sum _ { k = 3 } ^ { 6 } ( 2 k - 5 )$

Accepted Answer

A)  15 
B)  13 
C)  16 
D)  21 
A)  15 
B)  13 
C)  16 
D)  21

The sequence is defined recursively. Write the first four terms. -a1 = 1 and a_n = a_n- 1 - 3 for n ≥ 2

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

Find the indicated term using the given information. -a 13 = 80 , a16 = 98 ; a7

Express the sum using summation notation. - $\sum _ { k = 1 } ^ { 5 } ( k - 10 )$

Find the sum of the arithmetic sequence. -{3n + 7}, n = 48

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

Determine whether the sequence is arithmetic. -2, -1, -4, -7, -10, ...

An arithmetic sequence is given. Find the common difference and write out the first four terms. -{12 - 6n}

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is -2; 15th term is -18

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If geometric, find the common ratio. - $\left\{ \left( \frac { 6 } { 5 } \right) ^ { n } \right\}$

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

A geometric sequence is given. Find the common ratio and write out the first four terms. - $\left\{ 4 \left( \frac { 1 } { 2 } \right) ^ { n - 1 } \right\}$

Find the indicated term of the sequence. -The twentieth term of the arithmetic sequence -13, 23, 53, ...

Write out the first five terms of the sequence. -During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth year are $ 224,000, then what are the profits for each of the first four years?

Solve the problem. -A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?

Determine whether the sequence is arithmetic. -2, 4, 6, 10, 12, ...

Find the sum of the arithmetic sequence. -6 + 12 + 18 + ... + 492

Write out the first five terms of the sequence. -{2(4n - 3)}

Write out the first five terms of the sequence. -{3n - 1}

Express the sum using summation notation. - $\sum _ { k = 3 } ^ { 6 } ( 2 k - 5 )$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Counting and Probability

Filters

Exam 7: Sequences; Induction; the Binomial Theorem

The sequence is defined recursively. Write the first four terms. -a1 = 1 and an = an- 1 - 3 for n ≥ 2

Express the sum using summation notation. - ∑k=142k\sum _ { k = 1 } ^ { 4 } 2 ^ { k }∑k=14​2k

Find the indicated term using the given information. -a 13 = 80 , a16 = 98 ; a7

Express the sum using summation notation. - ∑k=15(k−10)\sum _ { k = 1 } ^ { 5 } ( k - 10 )∑k=15​(k−10)

Find the sum of the arithmetic sequence. -{3n + 7}, n = 48

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

Determine whether the sequence is arithmetic. -2, -1, -4, -7, -10, ...

An arithmetic sequence is given. Find the common difference and write out the first four terms. -{12 - 6n}

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is -2; 15th term is -18

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If geometric, find the common ratio. - {(65)n}\left\{ \left( \frac { 6 } { 5 } \right) ^ { n } \right\}{(56​)n}

Express the sum using summation notation. - ∑k=14(−14)k\sum _ { k = 1 } ^ { 4 } \left( - \frac { 1 } { 4 } \right) ^ { k }∑k=14​(−41​)k

A geometric sequence is given. Find the common ratio and write out the first four terms. - {4(12)n−1}\left\{ 4 \left( \frac { 1 } { 2 } \right) ^ { n - 1 } \right\}{4(21​)n−1}

Find the indicated term of the sequence. -The twentieth term of the arithmetic sequence -13, 23, 53, ...

Write out the first five terms of the sequence. -During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth year are $ 224,000, then what are the profits for each of the first four years?

Solve the problem. -A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?

Determine whether the sequence is arithmetic. -2, 4, 6, 10, 12, ...

Find the sum of the arithmetic sequence. -6 + 12 + 18 + ... + 492

Write out the first five terms of the sequence. -{2(4n - 3)}

Write out the first five terms of the sequence. -{3n - 1}

Express the sum using summation notation. - ∑k=36(2k−5)\sum _ { k = 3 } ^ { 6 } ( 2 k - 5 )∑k=36​(2k−5)

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Counting and Probability

Filters

The sequence is defined recursively. Write the first four terms. -a1 = 1 and a_n = a_n- 1 - 3 for n ≥ 2

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

Express the sum using summation notation. - $\sum _ { k = 1 } ^ { 5 } ( k - 10 )$

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If geometric, find the common ratio. - $\left\{ \left( \frac { 6 } { 5 } \right) ^ { n } \right\}$

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

A geometric sequence is given. Find the common ratio and write out the first four terms. - $\left\{ 4 \left( \frac { 1 } { 2 } \right) ^ { n - 1 } \right\}$

Express the sum using summation notation. - $\sum _ { k = 3 } ^ { 6 } ( 2 k - 5 )$