Question 1

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$$3 + 6 + 9 + \ldots + 27$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 9 } 3 i ^ { 2 }$ 
B)  $\sum _ { i = 0 } ^ { 9 } 3 i$ 
C)  $\sum _ { i = 1 } ^ { 9 } 3 i$ 
D)  $\sum _ { i = 1 } ^ { 9 } i ^ { 2 }$ 
A)  $\sum _ { i = 1 } ^ { 9 } 3 i ^ { 2 }$ 
B)  $\sum _ { i = 0 } ^ { 9 } 3 i$ 
C)  $\sum _ { i = 1 } ^ { 9 } 3 i$ 
D)  $\sum _ { i = 1 } ^ { 9 } i ^ { 2 }$

Question 2

Find the indicated sum.
-$$\sum _ { i = 3 } ^ { 6 } \frac { i ! } { ( i - 1 ) ! }$$

Accepted Answer

A)  3 
B)  18 
C)  10 
D)  6 
A)  3 
B)  18 
C)  10 
D)  6

Question 3

Write the first four terms of the sequence whose general term is given.
-an = (-1)n + 1(n + 9)

Accepted Answer

A)  -10, 11, -12, 13 
B)  10, -22, 36, -52 
C)  -11, 12, -13, 14 
D)  10, -11, 12, -13 
A)  -10, 11, -12, 13 
B)  10, -22, 36, -52 
C)  -11, 12, -13, 14 
D)  10, -11, 12, -13

Question 4

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = ( - 1 ) ^ { n + 1 } ( n + 9 )$$

Accepted Answer

A)  $- 10,11 , - 12,13$ 
B)  $10 , - 22,36 , - 52$ 
C)  $- 11,12 , - 13,14$ 
D)  $10 , - 11,12 , - 13$ 
A)  $- 10,11 , - 12,13$ 
B)  $10 , - 22,36 , - 52$ 
C)  $- 11,12 , - 13,14$ 
D)  $10 , - 11,12 , - 13$

Question 5

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
-$$4 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + \frac { 17 } { 2 }$$

Accepted Answer

A)  $\sum _ { k = 2 } ^ { 17 } \frac { k } { 2 }$ 
B)  $\sum _ { k = 8 } ^ { 17 } \frac { k } { 2 }$ 
C)  $\sum _ { k = 8 } ^ { 12 } \frac { k } { 2 }$ 
D)  $\sum _ { k = 1 } ^ { 17 } \frac { \mathrm { k } } { 2 }$ 
A)  $\sum _ { k = 2 } ^ { 17 } \frac { k } { 2 }$ 
B)  $\sum _ { k = 8 } ^ { 17 } \frac { k } { 2 }$ 
C)  $\sum _ { k = 8 } ^ { 12 } \frac { k } { 2 }$ 
D)  $\sum _ { k = 1 } ^ { 17 } \frac { \mathrm { k } } { 2 }$

Question 6

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$$\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 6 } { 7 }$$

Accepted Answer

A)  $\sum _ { i = 2 } ^ { 12 } \frac { i } { i + 1 }$ 
B)  $\sum _ { i = 1 } ^ { n } \frac { i } { i + 2 }$ 
C)  $\sum _ { i = 0 } ^ { 12 } \frac { i } { i + 2 }$ 
D)  $\sum _ { i = 1 } ^ { 12 } \frac { i } { i + 2 }$ 
A)  $\sum _ { i = 2 } ^ { 12 } \frac { i } { i + 1 }$ 
B)  $\sum _ { i = 1 } ^ { n } \frac { i } { i + 2 }$ 
C)  $\sum _ { i = 0 } ^ { 12 } \frac { i } { i + 2 }$ 
D)  $\sum _ { i = 1 } ^ { 12 } \frac { i } { i + 2 }$

Question 7

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find 2 + 4 + 6 + 8 + . . ., the sum of the first 40 positive even integers.

Accepted Answer

A)  1644 
B)  1599 
C)  1640 
D)  1595 
A)  1644 
B)  1599 
C)  1640 
D)  1595

Question 8

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-Find a8 when a1 = 2,000,000, r = 0.1.

Accepted Answer

A)  0.002 
B)  2 
C)  0.02 
D)  0.2 
A)  0.002 
B)  2 
C)  0.02 
D)  0.2

Question 9

Write a formula for the general term (the nth term) of the geometric sequence.
-$6,12,24,48,96 , \ldots$

Accepted Answer

A)  $a _ { n } = 6 ( 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = a _ { 1 } + 2 ^ { n }$ 
C)  $a _ { n } = 6 ( 2 n )$ 
D)  $a _ { n } = 6 ( 2 ) ^ { \mathrm { n } }$ 
A)  $a _ { n } = 6 ( 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = a _ { 1 } + 2 ^ { n }$ 
C)  $a _ { n } = 6 ( 2 n )$ 
D)  $a _ { n } = 6 ( 2 ) ^ { \mathrm { n } }$

Question 10

Find the indicated sum.
-$$\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 6 i }$$

Accepted Answer

A)  $\frac { 1 } { 24 }$ 
B)  $\frac { 11 } { 36 }$ 
C)  $\frac { 25 } { 72 }$ 
D)  $\frac { 5 } { 24 }$ 
A)  $\frac { 1 } { 24 }$ 
B)  $\frac { 11 } { 36 }$ 
C)  $\frac { 25 } { 72 }$ 
D)  $\frac { 5 } { 24 }$

Question 11

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-Find a 10 when a $1 = 1000 , r = \frac { 1 } { 3 }$.

Accepted Answer

A)  $\frac { 1000 } { 59,049 }$ 
B)  $\frac { 1000 } { 19,683 }$ 
C)  $\frac { 1000 } { 177,147 }$ 
D)  1003 
A)  $\frac { 1000 } { 59,049 }$ 
B)  $\frac { 1000 } { 19,683 }$ 
C)  $\frac { 1000 } { 177,147 }$ 
D)  1003

Question 12

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the odd integers between 22 and 52.

Accepted Answer

A)  592 
B)  555 
C)  518 
D)  629 
A)  592 
B)  555 
C)  518 
D)  629

Question 13

Write a formula for the general term (the nth term) of the geometric sequence.
-$- 8 , - 16 , - 32 , - 64 , - 128 , \ldots$

Accepted Answer

A)  $a _ { n } = - 8 ( 2 n )$ 
B)  $a _ { n } = - 8 ( 2 ) ^ { n }$ 
C)  $a _ { n } = - 8 ( 2 ) ^ { n - 1 }$ 
D)  $a _ { n } = a _ { 1 } + 2 ^ { n }$ 
A)  $a _ { n } = - 8 ( 2 n )$ 
B)  $a _ { n } = - 8 ( 2 ) ^ { n }$ 
C)  $a _ { n } = - 8 ( 2 ) ^ { n - 1 }$ 
D)  $a _ { n } = a _ { 1 } + 2 ^ { n }$

Question 14

Find the indicated sum.
-$$\sum _ { i = 1 } ^ { 4 } 2 ^ { i }$$

Accepted Answer

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

Question 15

Write a formula for the general term (the nth term) of the geometric sequence.
-$3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$

Accepted Answer

A)  $a _ { n } = 3 \left( \frac { 1 } { 9 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n }$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 3 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { n } - 1 }$ 
D)  $a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n + 1 }$ 
A)  $a _ { n } = 3 \left( \frac { 1 } { 9 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n }$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 3 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { n } - 1 }$ 
D)  $a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n + 1 }$

Question 16

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-$$\text { Find } a _ { 4 } \text { when } a _ { 1 } = 2 , r = 5 \text {. }$$

Accepted Answer

A)  30 
B)  1250 
C)  125 
D)  250 
A)  30 
B)  1250 
C)  125 
D)  250

Question 17

Solve the problem.
-A person puts $27 into a bank account on January 1, $32 on February 1, $37 on March 1, and so forth. How much has the person put into the bank account by December 30?

Accepted Answer

A)  $1308 
B)  $684 
C)  $654 
D)  $492 
A)  $1308 
B)  $684 
C)  $654 
D)  $492

Question 18

Find the common ratio for the geometric sequence.
-80, 40, 20, 10, 5, . . .

Accepted Answer

A)  0.5 
B)  -0.5 
C)  2 
D)  5 
A)  0.5 
B)  -0.5 
C)  2 
D)  5

Question 19

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 31 } ( - 4 i - 8 )$$

Accepted Answer

A)  $- 2092.5$ 
B)  $- 2170$ 
C)  $- 2232$ 
D)  $- 1984$ 
A)  $- 2092.5$ 
B)  $- 2170$ 
C)  $- 2232$ 
D)  $- 1984$

Question 20

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
-$$\mathrm { a } _ { 1 } = - 28 ; \mathrm { d } = 6$$

Accepted Answer

A)  $- 16 , - 22 , - 28 , - 34 , - 40$ 
B)  $- 28 , - 22 , - 16 , - 10 , - 4$ 
C)  $- 4 , - 10 , - 16 , - 22 , - 28$ 
D)  $- 16 , - 10 , - 4,2,8$ 
A)  $- 16 , - 22 , - 28 , - 34 , - 40$ 
B)  $- 28 , - 22 , - 16 , - 10 , - 4$ 
C)  $- 4 , - 10 , - 16 , - 22 , - 28$ 
D)  $- 16 , - 10 , - 4,2,8$

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $3 + 6 + 9 + \ldots + 27$

Find the indicated sum. - $\sum _ { i = 3 } ^ { 6 } \frac { i ! } { ( i - 1 ) ! }$

Write the first four terms of the sequence whose general term is given. -a_n = (-1)^{n + 1}(n + 9)

Write the first four terms of the sequence whose general term is given. - $a _ { n } = ( - 1 ) ^ { n + 1 } ( n + 9 )$

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $4 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + \frac { 17 } { 2 }$

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 6 } { 7 }$

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find 2 + 4 + 6 + 8 + . . ., the sum of the first 40 positive even integers.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a8 when a1 = 2,000,000, r = 0.1.

Write a formula for the general term (the nth term) of the geometric sequence. - $6,12,24,48,96 , \ldots$

Find the indicated sum. - $\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 6 i }$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a 10 when a $1 = 1000 , r = \frac { 1 } { 3 }$ .

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the odd integers between 22 and 52.

Write a formula for the general term (the nth term) of the geometric sequence. - $- 8 , - 16 , - 32 , - 64 , - 128 , \ldots$

Find the indicated sum. - $\sum _ { i = 1 } ^ { 4 } 2 ^ { i }$

Write a formula for the general term (the nth term) of the geometric sequence. - $3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. - $\text { Find } a _ { 4 } \text { when } a _ { 1 } = 2 , r = 5 \text {. }$

Solve the problem. -A person puts $27 into a bank account on January 1, $32 on February 1, $37 on March 1, and so forth. How much has the person put into the bank account by December 30?

Find the common ratio for the geometric sequence. -80, 40, 20, 10, 5, . . .

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { i = 1 } ^ { 31 } ( - 4 i - 8 )$

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d. - $\mathrm { a } _ { 1 } = - 28 ; \mathrm { d } = 6$

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Exam 8: Quadratic Equations and Functions

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - 3+6+9+…+273 + 6 + 9 + \ldots + 273+6+9+…+27

Find the indicated sum. - ∑i=36i!(i−1)!\sum _ { i = 3 } ^ { 6 } \frac { i ! } { ( i - 1 ) ! }∑i=36​(i−1)!i!​

Write the first four terms of the sequence whose general term is given. -an = (-1)n + 1(n + 9)

Write the first four terms of the sequence whose general term is given. - an=(−1)n+1(n+9)a _ { n } = ( - 1 ) ^ { n + 1 } ( n + 9 )an​=(−1)n+1(n+9)

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - 4+92+5+112+…+1724 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + \frac { 17 } { 2 }4+29​+5+211​+…+217​

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - 13+12+35+…+67\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 6 } { 7 }31​+21​+53​+…+76​