Question 1

Find the indicated sum.
-$$\sum _ { i = 1 } ^ { 5 } \frac { ( - 1 ) ^ { \mathrm { i } + 1 } } { ( \mathrm { i } + 2 ) ! }$$

Accepted Answer

A)  $\frac { 37 } { 280 }$ 
B)  $- \frac { 109 } { 420 }$ 
C)  $- \frac { 37 } { 280 }$ 
D)  $\frac { 109 } { 420 }$ 
A)  $\frac { 37 } { 280 }$ 
B)  $- \frac { 109 } { 420 }$ 
C)  $- \frac { 37 } { 280 }$ 
D)  $\frac { 109 } { 420 }$ A

Question 2

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \frac { - 4 ( n + 1 ) ! } { n ! }$$

Accepted Answer

A)  $- 8 , - 6 , - \frac { 8 } { 3 } , - \frac { 5 } { 6 }$ 
B)  $- 8 , - 6 , - \frac { 16 } { 3 } , - 5$ 
C)  $- 8 , - 12 , - 16 , - 20$ 
D)  $- 3 , - 2 , - 1,0$ 
A)  $- 8 , - 6 , - \frac { 8 } { 3 } , - \frac { 5 } { 6 }$ 
B)  $- 8 , - 6 , - \frac { 16 } { 3 } , - 5$ 
C)  $- 8 , - 12 , - 16 , - 20$ 
D)  $- 3 , - 2 , - 1,0$ C

Question 3

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the first eight terms of the arithmetic sequence: 3, 5, 7, . . . .

Accepted Answer

A)  160 
B)  40 
C)  15 
D)  80 
A)  160 
B)  40 
C)  15 
D)  80 D

Question 4

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d.
-$$a _ { 1 } = - \frac { 3 } { 5 } , d = \frac { 4 } { 5 }$$

Accepted Answer

A)  $a _ { n } = \frac { 4 } { 5 } n - \frac { 7 } { 5 } ; a _ { 20 } = \frac { 73 } { 5 }$ 
B)  $a _ { n } = - \frac { 3 } { 5 } n + \frac { 7 } { 5 } ; a _ { 20 } = - \frac { 53 } { 5 }$ 
C)  $a _ { n } = \frac { 4 } { 5 } n - \frac { 3 } { 5 } ; a _ { 20 } = \frac { 77 } { 5 }$ 
D)  $a _ { n } = - \frac { 3 } { 5 } n + \frac { 4 } { 5 } ; a _ { 20 } = - \frac { 56 } { 5 }$ 
A)  $a _ { n } = \frac { 4 } { 5 } n - \frac { 7 } { 5 } ; a _ { 20 } = \frac { 73 } { 5 }$ 
B)  $a _ { n } = - \frac { 3 } { 5 } n + \frac { 7 } { 5 } ; a _ { 20 } = - \frac { 53 } { 5 }$ 
C)  $a _ { n } = \frac { 4 } { 5 } n - \frac { 3 } { 5 } ; a _ { 20 } = \frac { 77 } { 5 }$ 
D)  $a _ { n } = - \frac { 3 } { 5 } n + \frac { 4 } { 5 } ; a _ { 20 } = - \frac { 56 } { 5 }$

Question 5

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
-$$a _ { 1 } = - 5 ; r = 4$$

Accepted Answer

A)  $- 5 , - 1,3,7 , \ldots$ 
B)  $- 5 , - 20 , - 80 , - 320 , \ldots$ 
C)  $- 20 , - 80 , - 320 , - 1280 , \ldots$ 
D)  $- 5,20 , - 80,320 , \ldots$ 
A)  $- 5 , - 1,3,7 , \ldots$ 
B)  $- 5 , - 20 , - 80 , - 320 , \ldots$ 
C)  $- 20 , - 80 , - 320 , - 1280 , \ldots$ 
D)  $- 5,20 , - 80,320 , \ldots$

Question 6

Find the common difference for the arithmetic sequence.
-8, 13, 18, 23, . . .

Accepted Answer

A)  3.75 
B)  15 
C)  5 
D)  8 
A)  3.75 
B)  15 
C)  5 
D)  8

Question 7

Find the common ratio for the geometric sequence.
-$3 , \frac { 9 } { 2 } , \frac { 27 } { 4 } , \frac { 81 } { 8 } , \ldots$

Accepted Answer

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

Question 8

Write the first four terms of the sequence whose general term is given.
-$$\mathrm { a } _ { \mathrm { n } } = \left( \frac { 2 } { 3 } \right) ^ { \mathrm { n } }$$

Accepted Answer

A)  $\frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$ 
B)  $\frac { 2 } { 3 } , \frac { 2 } { 6 } , \frac { 2 } { 9 } , \frac { 2 } { 12 }$ 
C)  $1 , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$ 
D)  $1 , \frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 }$ 
A)  $\frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$ 
B)  $\frac { 2 } { 3 } , \frac { 2 } { 6 } , \frac { 2 } { 9 } , \frac { 2 } { 12 }$ 
C)  $1 , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$ 
D)  $1 , \frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 }$

Question 9

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
-$$a _ { 1 } = - \frac { 2 } { 5 } , r = - 4$$

Accepted Answer

A)  $= \frac { 2 } { 5 } , \frac { 8 } { 5 } , - \frac { 32 } { 5 } , \frac { 128 } { 5 } , \ldots$ 
B)  $- \frac { 2 } { 5 } , \frac { 32 } { 25 } , \frac { 32 } { 125 } , \frac { 512 } { 625 } , \ldots$ 
C)  $- \frac { 2 } { 5 } , \frac { 8 } { 5 } , \frac { 32 } { 5 } , \frac { 128 } { 5 } , \ldots$ 
D)  $= \frac { 2 } { 5 } , \frac { 8 } { 25 } , \frac { 16 } { 125 } , \frac { 128 } { 625 } , \ldots$ 
A)  $= \frac { 2 } { 5 } , \frac { 8 } { 5 } , - \frac { 32 } { 5 } , \frac { 128 } { 5 } , \ldots$ 
B)  $- \frac { 2 } { 5 } , \frac { 32 } { 25 } , \frac { 32 } { 125 } , \frac { 512 } { 625 } , \ldots$ 
C)  $- \frac { 2 } { 5 } , \frac { 8 } { 5 } , \frac { 32 } { 5 } , \frac { 128 } { 5 } , \ldots$ 
D)  $= \frac { 2 } { 5 } , \frac { 8 } { 25 } , \frac { 16 } { 125 } , \frac { 128 } { 625 } , \ldots$

Question 10

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = n ^ { 2 } - n$$

Accepted Answer

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

Question 11

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d.
-Find a14 when a1 = 23, d = -3.

Accepted Answer

A)  -39 
B)  -19 
C)  62 
D)  -16 
A)  -39 
B)  -19 
C)  62 
D)  -16

Question 12

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \frac { n + 2 } { 2 n - 1 }$$

Accepted Answer

A)  $- 3 , \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$ 
B)  $3 , \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$ 
C)  $- 3 , - \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$ 
D)  $3 , - \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$ 
A)  $- 3 , \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$ 
B)  $3 , \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$ 
C)  $- 3 , - \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$ 
D)  $3 , - \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$

Question 13

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = ( - 2 ) ^ { n }$$

Accepted Answer

A)  $2 , - 4 , - 8 , - 16$ 
B)  $- 2,4 , - 8,16$ 
C)  $- 2 , - 4 , - 8 , - 16$ 
D)  $2 , - 4,8 , - 16$ 
A)  $2 , - 4 , - 8 , - 16$ 
B)  $- 2,4 , - 8,16$ 
C)  $- 2 , - 4 , - 8 , - 16$ 
D)  $2 , - 4,8 , - 16$

Question 14

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = ( - 1 ) ^ { n } ( n + 2 )$$

Accepted Answer

A)  $3,4,5,6$ 
B)  $- 3 , - 8 , - 15 , - 24$ 
C)  $- 3,4 , - 5,6$ 
D)  $- 3 , - 4 , - 5 , - 6$ 
A)  $3,4,5,6$ 
B)  $- 3 , - 8 , - 15 , - 24$ 
C)  $- 3,4 , - 5,6$ 
D)  $- 3 , - 4 , - 5 , - 6$

Question 15

Find the indicated sum.
-$$\sum _ { i = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { i }$$

Accepted Answer

A)  $- \frac { 1 } { 16 }$ 
B)  $\frac { 5 } { 16 }$ 
C)  $\frac { 15 } { 16 }$ 
D)  $- \frac { 5 } { 16 }$ 
A)  $- \frac { 1 } { 16 }$ 
B)  $\frac { 5 } { 16 }$ 
C)  $\frac { 15 } { 16 }$ 
D)  $- \frac { 5 } { 16 }$

Question 16

Find the indicated sum.
-$$\sum _ { k = 2 } ^ { 4 } \mathrm { k } ( \mathrm { k } + 11 )$$

Accepted Answer

A)  86 
B)  51 
C)  140 
D)  128 
A)  86 
B)  51 
C)  140 
D)  128

Question 17

Write a formula for the general term (the nth term) of the geometric sequence.
-$$\frac { 1 } { 8 } , - \frac { 1 } { 40 } , \frac { 1 } { 200 } , - \frac { 1 } { 1000 } , \ldots$$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 8 } - \frac { 1 } { 5 } ( n - 1 )$ 
B)  $a _ { n } = \frac { 1 } { 5 } \left( - \frac { 1 } { 8 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = \frac { 1 } { 8 } \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = \left( \frac { 1 } { 8 } \right) ^ { n - 1 } - \frac { 3 } { 20 }$ 
A)  $a _ { n } = \frac { 1 } { 8 } - \frac { 1 } { 5 } ( n - 1 )$ 
B)  $a _ { n } = \frac { 1 } { 5 } \left( - \frac { 1 } { 8 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = \frac { 1 } { 8 } \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = \left( \frac { 1 } { 8 } \right) ^ { n - 1 } - \frac { 3 } { 20 }$

Question 18

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d.
-Find a 37 when $a _ { 1 } = 5 , d = \frac { 2 } { 3 }$.

Accepted Answer

A)  $- \frac { 59 } { 3 }$ 
B)  $- 19$ 
C)  29 
D)  $\frac { 89 } { 3 }$ 
A)  $- \frac { 59 } { 3 }$ 
B)  $- 19$ 
C)  29 
D)  $\frac { 89 } { 3 }$

Question 19

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

Accepted Answer

A)  $\sum _ { i = 0 } ^ { 6 } \frac { a + i } { i }$ 
B)  $\sum _ { i = 1 } ^ { n } \frac { a + i } { i }$ 
C)  $\sum _ { i = 0 } ^ { n } \frac { a + i } { i }$ 
D)  $\sum _ { i = 1 } ^ { 6 } \frac { a + i } { i }$ 
A)  $\sum _ { i = 0 } ^ { 6 } \frac { a + i } { i }$ 
B)  $\sum _ { i = 1 } ^ { n } \frac { a + i } { i }$ 
C)  $\sum _ { i = 0 } ^ { n } \frac { a + i } { i }$ 
D)  $\sum _ { i = 1 } ^ { 6 } \frac { a + i } { i }$

Question 20

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the first 25 terms of the arithmetic sequence: -5, 2, 9, 16, . . . .

Accepted Answer

A)  1896 
B)  1650 
C)  2063 
D)  1975 
A)  1896 
B)  1650 
C)  2063 
D)  1975

Find the indicated sum. - $\sum _ { i = 1 } ^ { 5 } \frac { ( - 1 ) ^ { \mathrm { i } + 1 } } { ( \mathrm { i } + 2 ) ! }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { - 4 ( n + 1 ) ! } { n ! }$

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first eight terms of the arithmetic sequence: 3, 5, 7, . . . .

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. - $a _ { 1 } = - \frac { 3 } { 5 } , d = \frac { 4 } { 5 }$

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - $a _ { 1 } = - 5 ; r = 4$

Find the common difference for the arithmetic sequence. -8, 13, 18, 23, . . .

Find the common ratio for the geometric sequence. - $3 , \frac { 9 } { 2 } , \frac { 27 } { 4 } , \frac { 81 } { 8 } , \ldots$

Write the first four terms of the sequence whose general term is given. - $\mathrm { a } _ { \mathrm { n } } = \left( \frac { 2 } { 3 } \right) ^ { \mathrm { n } }$

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - $a _ { 1 } = - \frac { 2 } { 5 } , r = - 4$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = n ^ { 2 } - n$

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a₁₄ when a₁ = 23, d = -3.

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { n + 2 } { 2 n - 1 }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = ( - 2 ) ^ { n }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = ( - 1 ) ^ { n } ( n + 2 )$

Find the indicated sum. - $\sum _ { i = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { i }$

Find the indicated sum. - $\sum _ { k = 2 } ^ { 4 } \mathrm { k } ( \mathrm { k } + 11 )$

Write a formula for the general term (the nth term) of the geometric sequence. - $\frac { 1 } { 8 } , - \frac { 1 } { 40 } , \frac { 1 } { 200 } , - \frac { 1 } { 1000 } , \ldots$

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a ₃₇ when $a _ { 1 } = 5 , d = \frac { 2 } { 3 }$ .

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

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first 25 terms of the arithmetic sequence: -5, 2, 9, 16, . . . .

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Exam 8: Quadratic Equations and Functions

Find the indicated sum. - ∑i=15(−1)i+1(i+2)!\sum _ { i = 1 } ^ { 5 } \frac { ( - 1 ) ^ { \mathrm { i } + 1 } } { ( \mathrm { i } + 2 ) ! }∑i=15​(i+2)!(−1)i+1​

Write the first four terms of the sequence whose general term is given. - an=−4(n+1)!n!a _ { n } = \frac { - 4 ( n + 1 ) ! } { n ! }an​=n!−4(n+1)!​

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first eight terms of the arithmetic sequence: 3, 5, 7, . . . .

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. - a1=−35,d=45a _ { 1 } = - \frac { 3 } { 5 } , d = \frac { 4 } { 5 }a1​=−53​,d=54​

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - a1=−5;r=4a _ { 1 } = - 5 ; r = 4a1​=−5;r=4

Find the common difference for the arithmetic sequence. -8, 13, 18, 23, . . .

Find the common ratio for the geometric sequence. - 3,92,274,818,…3 , \frac { 9 } { 2 } , \frac { 27 } { 4 } , \frac { 81 } { 8 } , \ldots3,29​,427​,881​,…

Write the first four terms of the sequence whose general term is given. - an=(23)n\mathrm { a } _ { \mathrm { n } } = \left( \frac { 2 } { 3 } \right) ^ { \mathrm { n } }an​=(32​)n

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - a1=−25,r=−4a _ { 1 } = - \frac { 2 } { 5 } , r = - 4a1​=−52​,r=−4

Write the first four terms of the sequence whose general term is given. - an=n2−na _ { n } = n ^ { 2 } - nan​=n2−n

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a14 when a1 = 23, d = -3.

Write the first four terms of the sequence whose general term is given. - an=n+22n−1a _ { n } = \frac { n + 2 } { 2 n - 1 }an​=2n−1n+2​

Write the first four terms of the sequence whose general term is given. - an=(−2)na _ { n } = ( - 2 ) ^ { n }an​=(−2)n

Write the first four terms of the sequence whose general term is given. - an=(−1)n(n+2)a _ { n } = ( - 1 ) ^ { n } ( n + 2 )an​=(−1)n(n+2)

Find the indicated sum. - ∑i=14(−12)i\sum _ { i = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { i }∑i=14​(−21​)i

Find the indicated sum. - ∑k=24k(k+11)\sum _ { k = 2 } ^ { 4 } \mathrm { k } ( \mathrm { k } + 11 )∑k=24​k(k+11)

Write a formula for the general term (the nth term) of the geometric sequence. - 18,−140,1200,−11000,…\frac { 1 } { 8 } , - \frac { 1 } { 40 } , \frac { 1 } { 200 } , - \frac { 1 } { 1000 } , \ldots81​,−401​,2001​,−10001​,…

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a 37 when a1=5,d=23a _ { 1 } = 5 , d = \frac { 2 } { 3 }a1​=5,d=32​ .

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - a+1+a+22+…+a+66a + 1 + \frac { a + 2 } { 2 } + \ldots + \frac { a + 6 } { 6 }a+1+2a+2​+…+6a+6​