1. Fundamental Concepts of Algebra

2. Equations and Inequalities

3. Functions and Graphs

4. Polynomial and Rational Functions

5. Exponential and Logarithmic Functions

6. Systems of Equations and Inequalities

7. Matrices and Determinants

8. Conic Sections

9. Sequences, Induction, and Probability

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

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

Writing a Geometric Series using Sigma / Summation Notation

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

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)

Use Recursion Formulas

Sequences and Summation Notation

Recursive Sequences

Factorials ; Evaluating Expressions With Factorials

In Exercises 61–68, use the graphs of and to find each indicated sum. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/35d5c023614ed0a4-1677154113361.jpg" alt="" /><img src="https://lightcat-files.s3.amazonaws.com/problem_images/aeef3edef6cb572f-1677154047518.jpg" alt="" /> 5Σi=1 (a_i+3b_i)

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

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

Use explicit rules to write sequences recursively

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

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

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

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)

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

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

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

In Exercises 61–68, use the graphs of and to find each indicated sum. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/aba2892c5d8bae8d-1677261198846.jpg" alt="" /> 5Σi=1 (a_i^2+1)

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)

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

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

Summation Notation

In Exercises 61–68, use the graphs of and to find each indicated sum. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/f8d294df5732f5ca-1677153951563.jpg" alt="" /><img src="https://lightcat-files.s3.amazonaws.com/problem_images/2d9ac0c89ebbe46d-1677153967805.jpg" alt="" /> 5Σi=4 (a_i/b_i)^2

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.

In Exercises 61–68, use the graphs of and to find each indicated sum. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/326cf704963a3936-1677261348507.jpg" alt="" /><img src="https://lightcat-files.s3.amazonaws.com/problem_images/0199e0be6703b5d4-1677261429778.jpg" alt="" /> 5∑i=1 (2a_i+b_i)

Writing Terms of a Sequence Given the General Term

Finding Terms in a Sequence Given the General Term

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

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

Writing The First Four Terms of a Sequence

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

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

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

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

Create a recursive formula

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

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

Sequences, Factorials, and Summation Notation

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

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

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

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

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

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

Factorials - Evaluating Factorials! Basic Info

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

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

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

In Exercises 61–68, use the graphs of and to find each indicated sum. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/8b67c6a44b057687-1677153938415.jpg" alt="" /><img src="https://lightcat-files.s3.amazonaws.com/problem_images/144c0f6a1b3922dc-1677153982704.jpg" alt="" /> 5Σi=4 (a_i/b_i)^3

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

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)!

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

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

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

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

In Exercises 61–68, use the graphs of and to find each indicated sum. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/77c790e7fb7250ca-1677154188207.jpg" alt="" /><img src="https://lightcat-files.s3.amazonaws.com/problem_images/ffc7c746e61b058f-1677154204466.jpg" alt="" /> 5Σi=1 a_i^2−5Σi=3 b_i^2

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!

In Exercises 61–68, use the graphs of and to find each indicated sum. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/25240f2a8e2c6439-1677154178035.jpg" alt="" /><img src="https://lightcat-files.s3.amazonaws.com/problem_images/712873ab2406fdf7-1677154232541.jpg" alt="" /> 5Σi=1 a_i^2+5Σi=1 b_i^2

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

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College Algebra

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Find the Common Difference for an Arithmetic Sequence

Write Terms of an Arithmetic Sequence

Use the Formula for the General Term of an Arithmetic Sequence

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence

Arithmetic Sequences

Compute Empirical Probability

Compute Theoretical Probability

Find the Probability that an Event will Not Occur

Find the Probability of One Event or a Second Event Occurring

Find the Probability of One Event and a Second Event Occurring

Probability

Evaluate a Binomial Coefficient

Expand a Binomial Raised to a Power

The Binomial Theorem

Use the Fundamental Counting Principle

Distinguish Between Permutation and Combination Problems