Exam 8: Quadratic Equations and Functions

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 = 20,000, r = -0.1.

(Multiple Choice)

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Question 101

Find the indicated sum. - $\sum _ { i = 3 } ^ { 8 } 12$

(Multiple Choice)

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Question 102

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

(Multiple Choice)

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Question 103

Find the common difference for the arithmetic sequence. -6, 10, 14, 18, . . .

(Multiple Choice)

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Question 104

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)$

(Multiple Choice)

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Question 105

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. - $\text { Find } a _ { 4 } \text { when } a _ { 1 } = 8 , r = - 5 \text {. }$

(Multiple Choice)

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Question 106

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 ₃₂ when a1 = 3 , d = -4 .

(Multiple Choice)

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Question 107

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 a₉ when a₁ = -4, r = 2.

(Multiple Choice)

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Question 108

Find the indicated sum. - $\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } - 5 \right)$

(Multiple Choice)

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Question 109

Write the first four terms of the sequence whose general term is given. - $a _ { n } = 3 ^ { n }$

(Multiple Choice)

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Question 110

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \left( - \frac { 3 } { 4 } \right) ^ { n }$

(Multiple Choice)

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Question 111

Find the common ratio for the geometric sequence. - $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$

(Multiple Choice)

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Question 112

Solve the problem. -The finite sequence whose general term is an = 0.13n² - 1.09n + 7.03, where n = 1, 2, 3, . . ., 9 models the total operating costs, in millions of dollars, for a company for nine consecutive years. Find $\sum _ { \mathrm { i } = 1 } ^ { 4 } \mathrm { a } _ { \mathrm { i } }$

(Multiple Choice)

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Question 113

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 a₅₀ when a₁ = -9, d = 3.

(Multiple Choice)

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Question 114

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { 4 } { n ^ { 2 } }$

(Multiple Choice)

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Question 115

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 = 20,000, r = -0.1.

Find the indicated sum. - $\sum _ { i = 3 } ^ { 8 } 12$

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

Find the common difference for the arithmetic sequence. -6, 10, 14, 18, . . .

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)$

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. - $\text { Find } a _ { 4 } \text { when } a _ { 1 } = 8 , r = - 5 \text {. }$

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 ₃₂ when a1 = 3 , d = -4 .

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 a₉ when a₁ = -4, r = 2.

Find the indicated sum. - $\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } - 5 \right)$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = 3 ^ { n }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \left( - \frac { 3 } { 4 } \right) ^ { n }$

Find the common ratio for the geometric sequence. - $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$

Solve the problem. -The finite sequence whose general term is an = 0.13n² - 1.09n + 7.03, where n = 1, 2, 3, . . ., 9 models the total operating costs, in millions of dollars, for a company for nine consecutive years. Find $\sum _ { \mathrm { i } = 1 } ^ { 4 } \mathrm { a } _ { \mathrm { i } }$

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 a₅₀ when a₁ = -9, d = 3.

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { 4 } { n ^ { 2 } }$

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Exam 8: Quadratic Equations and Functions

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 = 20,000, r = -0.1.

Find the indicated sum. - ∑i=3812\sum _ { i = 3 } ^ { 8 } 12∑i=38​12

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

Find the common difference for the arithmetic sequence. -6, 10, 14, 18, . . .

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - (a+1)+(a+b)+(a+b2)+…+(a+bn)( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)(a+1)+(a+b)+(a+b2)+…+(a+bn)

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 32 when a1 = 3 , d = -4 .

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 a9 when a1 = -4, r = 2.

Find the indicated sum. - ∑i=35(i2−5)\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } - 5 \right)∑i=35​(i2−5)

Write the first four terms of the sequence whose general term is given. - an=3na _ { n } = 3 ^ { n }an​=3n

Write the first four terms of the sequence whose general term is given. - an=(−34)na _ { n } = \left( - \frac { 3 } { 4 } \right) ^ { n }an​=(−43​)n

Find the common ratio for the geometric sequence. - 43,163,643,2563,10243,…\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots34​,316​,364​,3256​,31024​,…

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 a50 when a1 = -9, d = 3.

Write the first four terms of the sequence whose general term is given. - an=4n2a _ { n } = \frac { 4 } { n ^ { 2 } }an​=n24​

Algebra, Mathematical Models, and Problem Solving

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Find the indicated sum. - $\sum _ { i = 3 } ^ { 8 } 12$

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

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)$

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 ₃₂ when a1 = 3 , d = -4 .

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 a₉ when a₁ = -4, r = 2.

Find the indicated sum. - $\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } - 5 \right)$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = 3 ^ { n }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \left( - \frac { 3 } { 4 } \right) ^ { n }$

Find the common ratio for the geometric sequence. - $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$

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 a₅₀ when a₁ = -9, d = 3.

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { 4 } { n ^ { 2 } }$