Question 1

Find the indicated term using the given information.
-a = 8 , d = 3 ; a34

Accepted Answer

A)  -94 
B)  -91 
C)  107 
D)  110

Question 2

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

Accepted Answer

A)  5, 9, 8, 7 
B)  8, 16, 32, 64 
C)  5, 12, 22, 42 
D)  5, 10, 20, 40

Question 3

The sequence is defined recursively. Write the first four terms.
-$a _ { 1 } = \sqrt { 6 } ; a _ { n } = \sqrt { 6 a _ { n - 1 } }$

Accepted Answer

A)  $\sqrt { 6 } , \sqrt { 6 \sqrt { 6 } } , \sqrt { 6 \sqrt { 6 \sqrt { 6 } } } , \sqrt { 6 \sqrt { 6 \sqrt { 6 \sqrt { 6 } } } }$ 
B)  $\sqrt { 6 } , 6 \sqrt { 6 } , 36 \sqrt { 6 } , 216 \sqrt { 6 }$ 
C)  $\sqrt { 6 } , 6,6 \sqrt { 6 } , 36$ 
D)  $\sqrt { 6 } , \sqrt { \sqrt { 6 } } , \sqrt { \sqrt { \sqrt { 6 } } } , \sqrt { \sqrt { \sqrt { \sqrt { 6 } } } }$

Question 4

Evaluate the factorial expression.
-$\frac { ( n + 4 ) ! } { n + 4 }$

Accepted Answer

A)  1 
B)  $n + 4$ ! 
C)  $4 !$ 
D)  $( n + 3 ) !$

Question 5

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

Accepted Answer

A)  -1, 0, 1, 2, 3 
B)  -4, -3, -2, -1, 0 
C)  0, 1, 2, 3, 4 
D)  1, 2, 3, 4, 5

Question 6

Find the sum of the arithmetic sequence.
-{-5n + 5}, n = 29

Accepted Answer

A)  -1957.5 
B)  -1899.5 
C)  -2030 
D)  -1798

Question 7

The sequence is defined recursively. Write the first four terms.
-$a _ { 1 } = y ; a _ { n } = a _ { n - 1 } + U$

Accepted Answer

A)  $y , U , 2 U , 3 U$ 
B)  $y , y - U , y - 2 U , y - 3 U$ 
C)  $y , y + U , y + 2 U , y + 3 U$ 
D)  $U , U + y , U + 2 y , U + 3 y$

Question 8

Express the sum using summation notation.
-2 + 4 + 6 + ... + 16

Accepted Answer

A) 
$\sum _ { k = 1 } ^ { 8 } k ^ { 2 }$ 
B) 
$\sum _ { k = 0 } ^ { 8 } 2 k$ 
C) 
$\sum _ { k = 1 } ^ { 8 } 2 k ^ { 2 }$ 
D) 
$\sum _ { k = 1 } ^ { 8 } 2 k$

Question 9

Determine whether the sequence is arithmetic.
-4, 12, 36, 108, 972, ...

Accepted Answer

A)  Arithmetic 
B)  Not arithmetic

Question 10

Find the indicated term using the given information.
-$a _ { 14 } = - \frac { 17 } { 4 }$, a $_ { 24 } = - \frac { 37 } { 4 } ; a _ { 4 }$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $- 9$

Question 11

Express the sum using summation notation.
-$\sum _ { \mathrm { k } = 1 } ^ { 4 } ( - 1 ) ^ { \mathrm { k } } ( \mathrm { k } + 16 )$

Accepted Answer

A)  74 
B)  $- 74$ 
C)  66 
D)  2

Question 12

Write out the first five terms of the sequence.
-{n2 - n}

Accepted Answer

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

Question 13

Write out the sum. Do not evaluate.
-$\sum _ { k = 1 } ^ { 6 } ( 5 k - 2 )$

Accepted Answer

A)  65 
B)  $3 + 8 + 13 + 18 + 23 + 28 + \ldots$ 
C)  $1 + 3 + 8 + 13 + 18 + 23$ 
D)  $3 + 8 + 13 + 18 + 23 + 28$

Question 14

Find the sum of the arithmetic sequence.
-{-3n - 1}, n = 50

Accepted Answer

A)  -3700 
B)  -3875 
C)  -3525 
D)  -3800

Question 15

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-29, 17.4, 10.44, 6.264, 3.76

Accepted Answer

A)  3.76 
B)  1.67 
C)  0.6 
D)  -0.6

Question 16

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If
geometric, find the common ratio.
-{2n2}

Accepted Answer

A)  Geometric, r = 2 
B)  Geometric, r 2 
C)  Arithmetic, d = 2 
D)  Neither = 2

Question 17

Evaluate the factorial expression.
-$\frac { 7 ! } { 5 ! 2 ! }$

Accepted Answer

A)  0 ! 
B)  7 
C)  21 
D)  1

Question 18

Find the indicated term using the given information.
-a 17 = 34 , a11 = 16 ; a1

Accepted Answer

A)  -8 
B)  3 
C)  -14 
D)  -11

Question 19

Determine whether the sequence is geometric.
-$$\frac { 1 } { 8 } , \frac { 1 } { 11 } , \frac { 1 } { 14 } , \frac { 1 } { 17 } , \ldots$$

Accepted Answer

A)  Geometric 
B)  Not geometric

Question 20

Use a graphing utility to find the sum of each sequence.
-{ 3.6n + 8.83}, n=10

Accepted Answer

A)  241.47 
B)  286.3 
C)  44.83 
D)  41.23

Exam 7: Sequences; Induction; the Binomial Theorem

Find the indicated term using the given information. -a = 8 , d = 3 ; a34

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

The sequence is defined recursively. Write the first four terms. - $a _ { 1 } = \sqrt { 6 } ; a _ { n } = \sqrt { 6 a _ { n - 1 } }$

Evaluate the factorial expression. - $\frac { ( n + 4 ) ! } { n + 4 }$

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

Find the sum of the arithmetic sequence. -{-5n + 5}, n = 29

The sequence is defined recursively. Write the first four terms. - $a _ { 1 } = y ; a _ { n } = a _ { n - 1 } + U$

Express the sum using summation notation. -2 + 4 + 6 + ... + 16

Determine whether the sequence is arithmetic. -4, 12, 36, 108, 972, ...

Find the indicated term using the given information. - $a _ { 14 } = - \frac { 17 } { 4 }$ , a $_ { 24 } = - \frac { 37 } { 4 } ; a _ { 4 }$

Express the sum using summation notation. - $\sum _ { \mathrm { k } = 1 } ^ { 4 } ( - 1 ) ^ { \mathrm { k } } ( \mathrm { k } + 16 )$

Write out the first five terms of the sequence. -{n2 - n}

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 6 } ( 5 k - 2 )$

Find the sum of the arithmetic sequence. -{-3n - 1}, n = 50

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. -29, 17.4, 10.44, 6.264, 3.76

Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If geometric, find the common ratio. -{2n2}

Evaluate the factorial expression. - $\frac { 7 ! } { 5 ! 2 ! }$

Find the indicated term using the given information. -a 17 = 34 , a11 = 16 ; a1

Determine whether the sequence is geometric. - $\frac { 1 } { 8 } , \frac { 1 } { 11 } , \frac { 1 } { 14 } , \frac { 1 } { 17 } , \ldots$

Use a graphing utility to find the sum of each sequence. -{ 3.6n + 8.83}, n=10