9. Sequences, Series, & Induction

Sequences

9. Sequences, Series, & Induction

Sequences

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8:22

Introduction to Sequences

Writing a General Formula

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Finding Terms in a Sequence Given the General Term

01:51

Finding Terms in a Sequence Given the General Term

Writing The First Four Terms of a Sequence

The Organic Chemistry Tutor

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Arithmetic Sequences: A Formula for the ' n - th ' Term

11:06

Arithmetic Sequences: A Formula for the ' n - th ' Term

Factorials - Evaluating Factorials! Basic Info

Factorials ; Evaluating Expressions With Factorials

Writing a Geometric Series using Sigma / Summation Notation, Ex 2

Writing a Geometric Series using Sigma / Summation Notation

patrickJMT

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Multiple Choice

The first 4 terms of a sequence are $\left\lbrace\sqrt3,2\sqrt3,3\sqrt3,4\sqrt3,\ldots\right\rbrace$ . Continuing this pattern, find the $7^{\th}$ term.

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Multiple Choice

Determine the first 3 terms of the sequence given by the general formula

$a_{n}=\frac{1}{n!+1}$

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Multiple Choice

Write the first 6 terms of the sequence given by the recursive formula $a_{n}=a_{n-2}+a_{n-1}$ ; $a_1=1$ ; $a_2=1$ .

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Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3n+2

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Textbook Question

In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 7n - 4

185

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Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3^n

168

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Textbook Question

In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 1/(n - 1)!

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Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−3)^n

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Textbook Question

Evaluate 40!/(4! 38!)

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Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n(n+3)

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Textbook Question

In Exercises 8–9, find each indicated sum. This is a summation, refer to the textbook.

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Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=2n/(n+4)

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Textbook Question

In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 1/3 + 2/4 + 3/5 + ... + 15/17

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Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n+1/(2^n−1)

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Textbook Question

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=7 and a_n=a_n-1 + 5 for n≥2

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Textbook Question

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=3 and a_n=4a_n-1 for n≥2

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Textbook Question

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=4 and a_n=2a_n-1 + 3 for n≥2

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Textbook Question

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n = n^2/n!

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Textbook Question

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n=2(n+1)!

106

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Textbook Question

In Exercises 23–28, evaluate each factorial expression. 17!/15!

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Textbook Question

In Exercises 23–28, evaluate each factorial expression. 16!/2!14!

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Textbook Question

In Exercises 23–28, evaluate each factorial expression. (n+2)!/n!

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Textbook Question

In Exercises 29–42, find each indicated sum. 6Σi=1 5i

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Textbook Question

In Exercises 29–42, find each indicated sum. 4Σi=1 2i^2

102

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Textbook Question

In Exercises 29–42, find each indicated sum. 5Σk=1 k(k+4)

121

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Textbook Question

In Exercises 29–42, find each indicated sum. 4Σi=1 (−1/2)^i

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Textbook Question

In Exercises 29–42, find each indicated sum. 9Σi=5 11

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Textbook Question

In Exercises 29–42, find each indicated sum. 4Σi=0 (−1)^i/i!

122

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Textbook Question

In Exercises 29–42, find each indicated sum. 5Σi=1 i!/(i−1)!

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Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1^2+2^2+3^2+⋯+ 15^2

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Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 2+2^2+2^3+⋯+ 2^11

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Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

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Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1/2+2/3+3/4+⋯+ 14/(14+1)

121

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Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 4+4^2/2+4^3/3+⋯+ 4^n/n

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Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+3+5+⋯+ (2n−1)

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Textbook Question

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. 5+7+9+11+⋯+ 31

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Textbook Question

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+ar+ar2+⋯+ ar^12

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Textbook Question

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+(a+d)+(a+2d)+⋯+ (a+nd)

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Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 (a_i^2+1)

126

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Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

5∑i=1 (2a_i+b_i)

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Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 (a_i+3b_i)

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Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=4 (a_i/b_i)^2

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Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=4 (a_i/b_i)^3

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Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 a_i^2+5Σi=1 b_i^2

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Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 a_i^2−5Σi=3 b_i^2

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Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 200!/198!

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Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. (300/20)!

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Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/300

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Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/(20−3)!

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Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 54!/(54−3)!3!

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Textbook Question

Write the first five terms of the sequence whose first term is 9 and whose general term is an= (an−1)/2 if a_n-1 is even, a_n=3a_n-1 + 5 if a_n-1 is odd for n≥2.

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9. Sequences, Series, & Induction

Sequences

Learn with Patrick

Learn with other creators

Practice this topic