Exam 11: Sequences; Induction; the Binomial Theorem

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } 3 ( - 4 ) ^ { \mathrm { k } }$

(Multiple Choice)

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Question 221

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. - $a = 1 ; r = \frac { 1 } { 2 }$

(Multiple Choice)

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Question 222

Expand the expression using the Binomial Theorem. - $( 5 x + 3 ) ^ { 3 }$

(Multiple Choice)

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Question 223

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $\sum _ { k = 1 } ^ { \infty } 4 \left( \frac { 3 } { 2 } \right) ^ { k - 1 }$

(Multiple Choice)

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Question 224

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - $1,4,7,10,13 , \ldots$

(Multiple Choice)

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Question 225

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 9 \\ 5 \end{array} \right)$

(Multiple Choice)

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Question 226

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 3 k }$

(Multiple Choice)

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Question 227

Solve. -The number of students in a school in year $n$ is estimated by the model $a _ { n } = 7 n ^ { 2 } + 13 n + 81$ . About how many students are in the school in each of the first three years?

(Multiple Choice)

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Question 228

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $- 5 - 15 - 45 - 135 - 405 - \cdots - 5 \cdot 3 ^ { 9 }$

(Multiple Choice)

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Question 229

Express the sum using summation notation. - $2 + 4 + 6 + \cdots + 14$

(Multiple Choice)

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Question 230

Find the sum of the arithmetic sequence. -{6n + 8}, n = 46

(Multiple Choice)

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Question 231

Find the sum of the arithmetic sequence. -1 + 2 + 3 + ... + 329

(Multiple Choice)

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Question 232

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 5 \\ 2 \end{array} \right)$

(Multiple Choice)

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Question 233

Solve the problem. -As Sunee improves her algebra skills, she takes 0.9 times as long to complete each homework assignment as she took to complete the preceeding assignment. If it took her 55 minutes to complete her first assignment, find How long it took her to complete the fifth assignment. Find the total time she took to complete her first five Homework assignments. (Round to the nearest minute.)

(Multiple Choice)

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Question 234

Determine whether the sequence is geometric. -4, 12, 36, 108, 324, ...

(Multiple Choice)

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Question 235

Choose the one alternative that best completes the statement or answers the question. -Write 0.272727... as a fraction. (Find the sum of the repeating decimal.)

(Multiple Choice)

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Question 236

Solve. -The number of students in a school in year $n$ is estimated by the model $a _ { n } = 5 n ^ { 2 } + 14 n + 81$ . About how many students are in the school in each of the first three years?

(Multiple Choice)

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Question 237

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 a11 when a1 = -5, r = -3.

(Multiple Choice)

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Question 238

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } 3 ( - 4 ) ^ { \mathrm { k } }$

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. - $a = 1 ; r = \frac { 1 } { 2 }$

Expand the expression using the Binomial Theorem. - $( 5 x + 3 ) ^ { 3 }$

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $\sum _ { k = 1 } ^ { \infty } 4 \left( \frac { 3 } { 2 } \right) ^ { k - 1 }$

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - $1,4,7,10,13 , \ldots$

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 9 \\ 5 \end{array} \right)$

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 3 k }$

Solve. -The number of students in a school in year $n$ is estimated by the model $a _ { n } = 7 n ^ { 2 } + 13 n + 81$ . About how many students are in the school in each of the first three years?

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $- 5 - 15 - 45 - 135 - 405 - \cdots - 5 \cdot 3 ^ { 9 }$

Express the sum using summation notation. - $2 + 4 + 6 + \cdots + 14$

Find the sum of the arithmetic sequence. -{6n + 8}, n = 46

Find the sum of the arithmetic sequence. -1 + 2 + 3 + ... + 329

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 5 \\ 2 \end{array} \right)$

Determine whether the sequence is geometric. -4, 12, 36, 108, 324, ...

Choose the one alternative that best completes the statement or answers the question. -Write 0.272727... as a fraction. (Find the sum of the repeating decimal.)

Solve. -The number of students in a school in year $n$ is estimated by the model $a _ { n } = 5 n ^ { 2 } + 14 n + 81$ . About how many students are in the school in each of the first three years?

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 a11 when a1 = -5, r = -3.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 11: Sequences; Induction; the Binomial Theorem

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - ∑k=153(−4)k\sum _ { \mathrm { k } = 1 } ^ { 5 } 3 ( - 4 ) ^ { \mathrm { k } }∑k=15​3(−4)k

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. - a=1;r=12a = 1 ; r = \frac { 1 } { 2 }a=1;r=21​

Expand the expression using the Binomial Theorem. - (5x+3)3( 5 x + 3 ) ^ { 3 }(5x+3)3

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - ∑k=1∞4(32)k−1\sum _ { k = 1 } ^ { \infty } 4 \left( \frac { 3 } { 2 } \right) ^ { k - 1 }∑k=1∞​4(23​)k−1

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - 1,4,7,10,13,…1,4,7,10,13 , \ldots1,4,7,10,13,…

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - (95)\left( \begin{array} { l } 9 \\ 5 \end{array} \right)(95​)

Find the sum of the sequence. - ∑k=1413k\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 3 k }∑k=14​3k1​

Solve. -The number of students in a school in year nnn is estimated by the model an=7n2+13n+81a _ { n } = 7 n ^ { 2 } + 13 n + 81an​=7n2+13n+81 . About how many students are in the school in each of the first three years?

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - −5−15−45−135−405−⋯−5⋅39- 5 - 15 - 45 - 135 - 405 - \cdots - 5 \cdot 3 ^ { 9 }−5−15−45−135−405−⋯−5⋅39

Express the sum using summation notation. - 2+4+6+⋯+142 + 4 + 6 + \cdots + 142+4+6+⋯+14

Find the sum of the arithmetic sequence. -{6n + 8}, n = 46

Find the sum of the arithmetic sequence. -1 + 2 + 3 + ... + 329

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - (52)\left( \begin{array} { l } 5 \\ 2 \end{array} \right)(52​)

Determine whether the sequence is geometric. -4, 12, 36, 108, 324, ...

Choose the one alternative that best completes the statement or answers the question. -Write 0.272727... as a fraction. (Find the sum of the repeating decimal.)

Solve. -The number of students in a school in year nnn is estimated by the model an=5n2+14n+81a _ { n } = 5 n ^ { 2 } + 14 n + 81an​=5n2+14n+81 . About how many students are in the school in each of the first three years?

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 a11 when a1 = -5, r = -3.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } 3 ( - 4 ) ^ { \mathrm { k } }$

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. - $a = 1 ; r = \frac { 1 } { 2 }$

Expand the expression using the Binomial Theorem. - $( 5 x + 3 ) ^ { 3 }$

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $\sum _ { k = 1 } ^ { \infty } 4 \left( \frac { 3 } { 2 } \right) ^ { k - 1 }$

The given pattern continues. Write down the nth term of the sequence suggested by the pattern. - $1,4,7,10,13 , \ldots$

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 9 \\ 5 \end{array} \right)$

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 3 k }$

Solve. -The number of students in a school in year $n$ is estimated by the model $a _ { n } = 7 n ^ { 2 } + 13 n + 81$ . About how many students are in the school in each of the first three years?

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $- 5 - 15 - 45 - 135 - 405 - \cdots - 5 \cdot 3 ^ { 9 }$

Express the sum using summation notation. - $2 + 4 + 6 + \cdots + 14$

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 5 \\ 2 \end{array} \right)$

Solve. -The number of students in a school in year $n$ is estimated by the model $a _ { n } = 5 n ^ { 2 } + 14 n + 81$ . About how many students are in the school in each of the first three years?