Question 1

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence.
-6th term is -17; 15th term is -53

Accepted Answer

A)  a1 = 3, d = -4, an = an-1 - 4 
B)  a1 = 3, d = 4, an = an-1 + 4 
C)  a1 = 7, d = 4, an = an-1 + 4 
D)  a1 = 7, d = -4, an = an-1 - 4 
A)  a1 = 3, d = -4, an = an-1 - 4 
B)  a1 = 3, d = 4, an = an-1 + 4 
C)  a1 = 7, d = 4, an = an-1 + 4 
D)  a1 = 7, d = -4, an = an-1 - 4

Question 2

Find the sum of the sequence.
-$$\sum _ { k = 2 } ^ { 5 } ( 4 k - 5 )$$

Accepted Answer

A)  36 
B)  33 
C)  23 
D)  30 
A)  36 
B)  33 
C)  23 
D)  30

Question 3

Choose the one alternative that best completes the statement or answers the question.
-The coefficient of $x ^ { 8 }$ in the expansion of $\left( x ^ { 2 } - 3 \right) ^ { 7 }$

Accepted Answer

A)  945 
B)  $- 945$ 
C)  2835 
D)  $- 2835$ 
A)  945 
B)  $- 945$ 
C)  2835 
D)  $- 2835$

Question 4

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-$8,20,32,44,56 , \ldots$

Accepted Answer

A)  $a _ { n } = 8 ( 12 ) ^ { n - 1 }$ 
B)  $a _ { n } = 4 n - 12$ 
C)  $a _ { n } = 12 n - 1$ 
D)  $a _ { n } = 4 ( 3 n - 1 )$ 
A)  $a _ { n } = 8 ( 12 ) ^ { n - 1 }$ 
B)  $a _ { n } = 4 n - 12$ 
C)  $a _ { n } = 12 n - 1$ 
D)  $a _ { n } = 4 ( 3 n - 1 )$

Question 5

Find the value of the annuity with the following characteristics.
-Payments of $100 are made at the end of each year for 7 years at 4% interest compounded annually

Accepted Answer

A)  $3,289.83 
B)  $789.83 
C)  $663.30 
D)  $316.33 
A)  $3,289.83 
B)  $789.83 
C)  $663.30 
D)  $316.33

Question 6

Find the indicated term using the given information.
-$$a _ { 10 } = 35 , a _ { 18 } = 75 ; a _ { 1 }$$

Accepted Answer

A)  5 
B)  0 
C)  $- 5$ 
D)  $- 10$ 
A)  5 
B)  0 
C)  $- 5$ 
D)  $- 10$

Question 7

Determine whether the sequence is geometric.
-$$- \frac { 1 } { 4 } , - \frac { 1 } { 9 } , - \frac { 1 } { 14 } , - \frac { 1 } { 19 } , \ldots$$

Accepted Answer

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

Question 8

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-$$\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 }$$

Accepted Answer

A)  2 
B)  6 
C)  4 
D)  Not geometric 
A)  2 
B)  6 
C)  4 
D)  Not geometric

Question 9

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 10

Expand the expression using the Binomial Theorem.
-$$( x - 7 ) ^ { 5 }$$

Accepted Answer

A)  $x ^ { 5 } - 35 x ^ { 4 } + 980 x ^ { 3 } - 6,860 x ^ { 2 } + 12,005 x - 16,807$ 
B)  $x ^ { 5 } - 35 x ^ { 4 } + 490 x ^ { 3 } - 3,430 x ^ { 2 } + 12,005 x - 7$ 
C)  $x ^ { 5 } - 35 x ^ { 4 } + 490 x ^ { 3 } - 3,430 x ^ { 2 } + 12,005 x - 16,807$ 
D)  $x ^ { 5 } - 35 x ^ { 4 } + 980 x ^ { 3 } - 6,860 x ^ { 2 } + 12,005 x - 7$ 
A)  $x ^ { 5 } - 35 x ^ { 4 } + 980 x ^ { 3 } - 6,860 x ^ { 2 } + 12,005 x - 16,807$ 
B)  $x ^ { 5 } - 35 x ^ { 4 } + 490 x ^ { 3 } - 3,430 x ^ { 2 } + 12,005 x - 7$ 
C)  $x ^ { 5 } - 35 x ^ { 4 } + 490 x ^ { 3 } - 3,430 x ^ { 2 } + 12,005 x - 16,807$ 
D)  $x ^ { 5 } - 35 x ^ { 4 } + 980 x ^ { 3 } - 6,860 x ^ { 2 } + 12,005 x - 7$

Question 11

Solve the problem.
-A small business owner made $60,000 the first year he owned his store and made an additional 7% over the previous year in each subsequent year. Find how much he made during his fourth year of business. Find his
Total earnings during the first four years. (Round to the nearest cent, if necessary.)

Accepted Answer

A)  $294,780.00; $630,180.00 
B)  $501,126.00; $1,131,306.00 
C)  $20.58; $64,514.58 
D)  $73,502.58; $266,396.58 
A)  $294,780.00; $630,180.00 
B)  $501,126.00; $1,131,306.00 
C)  $20.58; $64,514.58 
D)  $73,502.58; $266,396.58

Question 12

Solve the problem.
-A brick staircase has a total of 19 steps The bottom step requires 141 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?

Accepted Answer

A)  3,534 bricks 
B)  1,776.5 bricks 
C)  1,824 bricks 
D)  3,648 bricks 
A)  3,534 bricks 
B)  1,776.5 bricks 
C)  1,824 bricks 
D)  3,648 bricks

Question 13

Find the indicated term of the sequence.
-The twentieth term of the arithmetic sequence $11,7,3 , \ldots$

Accepted Answer

A)  87 
B)  $- 69$ 
C)  91 
D)  $- 65$ 
A)  87 
B)  $- 69$ 
C)  91 
D)  $- 65$

Question 14

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence.
-8th term is 62; 13th term is 42

Accepted Answer

A)  a1 = 90, d = 4, an = an-1 + 4 
B)  a1 = 94, d = -4, an = an-1 - 4 
C)  a1 = 94, d = 4, an = an-1 + 4 
D)  a1 = 90, d = -4, an = an-1 - 4 
A)  a1 = 90, d = 4, an = an-1 + 4 
B)  a1 = 94, d = -4, an = an-1 - 4 
C)  a1 = 94, d = 4, an = an-1 + 4 
D)  a1 = 90, d = -4, an = an-1 - 4

Question 15

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are
given.
-$$\begin{array} { l } 
\mathrm { a } = 9 ; \mathrm { d } = - 9 \
\mathrm { a } _ { \mathrm { n } } = ? ; \mathrm { a } _ { 13 } = ?
\end{array}$$

Accepted Answer

A)  $a _ { n } = 18 - 9 n ; a _ { 13 } = - 99$ 
B)  $a _ { n } = 18 - 9 n ; a _ { 13 } = - 54$ 
C)  $a _ { n } = 9 - 9 n ; a _ { 13 } = - 99$ 
D)  $a _ { n } = 18 + 9 n ; a _ { 13 } = - 99$ 
A)  $a _ { n } = 18 - 9 n ; a _ { 13 } = - 99$ 
B)  $a _ { n } = 18 - 9 n ; a _ { 13 } = - 54$ 
C)  $a _ { n } = 9 - 9 n ; a _ { 13 } = - 99$ 
D)  $a _ { n } = 18 + 9 n ; a _ { 13 } = - 99$

Question 16

Choose the one alternative that best completes the statement or answers the question.
-After being struck with a hammer, a gong vibrates 54 vibrations in the first second and in each second thereafter makes 67 as many vibrations as in the previous second. Find how many vibrations the gong makes before it
Stops vibrating.

Accepted Answer

A)  388 vibrations 
B)  63 vibrations 
C)  58 vibrations 
D)  378 vibrations 
A)  388 vibrations 
B)  63 vibrations 
C)  58 vibrations 
D)  378 vibrations

Question 17

Find the sum.
-$$\sum _ { k = 1 } ^ { n } 5 \cdot 7 ^ { k - 1 }$$

Accepted Answer

A) $ - \frac { 5 } { 6 } \left( 1 - 7 ^ { n - 1 } \right)$ 
B)  $- 5 \left( 1 - 7 ^ { n } \right)$ 
C) $ = \frac { 5 } { 6 } \left( 1 - 7 ^ { n } \right)$ 
D)  $= 30 \left( 1 - 7 ^ { n } \right)$ 
A) $ - \frac { 5 } { 6 } \left( 1 - 7 ^ { n - 1 } \right)$ 
B)  $- 5 \left( 1 - 7 ^ { n } \right)$ 
C) $ = \frac { 5 } { 6 } \left( 1 - 7 ^ { n } \right)$ 
D)  $= 30 \left( 1 - 7 ^ { n } \right)$

Question 18

Find the sum of the arithmetic sequence.
-1 + 3 + 5 + ... + 1,109

Accepted Answer

A)  308,025 
B)  306,916 
C)  309,136 
D)  308,580 
A)  308,025 
B)  306,916 
C)  309,136 
D)  308,580

Question 19

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

Accepted Answer

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

Question 20

Find the nth term of the geometric sequence.
-$$a = 3 ; r = \left( \frac { 1 } { 3 } \right)$$

Accepted Answer

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

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -6th term is -17; 15th term is -53

Find the sum of the sequence. - $\sum _ { k = 2 } ^ { 5 } ( 4 k - 5 )$

Choose the one alternative that best completes the statement or answers the question. -The coefficient of $x ^ { 8 }$ in the expansion of $\left( x ^ { 2 } - 3 \right) ^ { 7 }$

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - $8,20,32,44,56 , \ldots$

Find the value of the annuity with the following characteristics. -Payments of $100 are made at the end of each year for 7 years at 4% interest compounded annually

Find the indicated term using the given information. - $a _ { 10 } = 35 , a _ { 18 } = 75 ; a _ { 1 }$

Determine whether the sequence is geometric. - $- \frac { 1 } { 4 } , - \frac { 1 } { 9 } , - \frac { 1 } { 14 } , - \frac { 1 } { 19 } , \ldots$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - $\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 }$

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

Expand the expression using the Binomial Theorem. - $( x - 7 ) ^ { 5 }$

Solve the problem. -A brick staircase has a total of 19 steps The bottom step requires 141 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?

Find the indicated term of the sequence. -The twentieth term of the arithmetic sequence $11,7,3 , \ldots$

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -8th term is 62; 13th term is 42

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. - =9;=-9 =?;=?

Find the sum. - $\sum _ { k = 1 } ^ { n } 5 \cdot 7 ^ { k - 1 }$

Find the sum of the arithmetic sequence. -1 + 3 + 5 + ... + 1,109

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

Find the nth term of the geometric sequence. - $a = 3 ; r = \left( \frac { 1 } { 3 } \right)$

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Exam 11: Sequences; Induction; the Binomial Theorem