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

undefined - Channels

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a60 when a₁ = 35, d = -3.

Arithmetic Progressions - Problem Solving

Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, ...

Arithmetic Progressions - Algebra

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/fbcfab590db875ee-1676482925308.jpg" alt="" /> If {a} is a finite sequence whose last term is -83, how many terms does {a} contain?

Use the formula a_n=4+(n-1)(-7) to find the eighth term of the sequence 4, −3, −10,…

Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/9f7b44cceeb4415e-1678243598836.jpg" style="width: 158px;">

In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2

Find the sum of the first 50 terms of the arithmetic sequence: -10, -6, -2, 2,....

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. an= an-1 -10, a₁ = 30

Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22,……….

In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= 5/2, d = -1/2

Finding the Sum of a Finite Arithmetic Series

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a50 when a₁ = 7, d = 5.

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. 1, 5, 9, 13,...

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1 = 9, d=2

Find the sum of the even integers between 21 and 45.

In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= -8, d=5

In Exercises 16–18, find the indicated term of the arithmetic sequence with first term, , and common difference, d. Find a12 when a1 = -8, d = -2

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

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. an = an-1 +3, a₁ = 4

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1=-20, d = -4

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/3431a144e3b91430-1676482545417.jpg" alt="" /> Find a14+b12.

Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. 7,3,-1,-5,...

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a200 when a₁ = −40, d = 5.

Quick Intro to Arithmetic Sequences

In Exercises 1–14, write the first six terms of each arithmetic sequence. a1 = 300, d= -90

Find the sum of the first 60 positive even integers.

Sequences, Factorials, and Summation Notation

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/f0d7c9ad47fb1c87-1678243618224.jpg" style="width: 154px;">

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/57d5d619d6dd4b91-1678243632775.jpg" style="width: 153px;">

In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?

In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a6 when a₁ = 13, d = 4.

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -10, a₁ = 30

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/17446aa163ce377a-1676484701067.jpg" alt="" /> Find the difference between the sum of the first 14 terms of {b} and the sum of the first 14 terms of {an}.

In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. -7, -3, 1, 5 ...

In Exercises 25–27, use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.  The  is a summation, refer to the textbook.

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6

In Exercises 1–14, write the first six terms of each arithmetic sequence. a₁ = 200, d = 20

Represent an arithmetic sequence as an explicit rule

Write Terms of an Arithmetic Sequence

Arithmetic Sequences

Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive multiples of 3.

Arithmetic Sequences: Finding a General Formula Given Two Terms

Find the sum of the odd integers between 30 and 54.

In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 +6, a₁ = −9

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

College Algebra

https://static.studychannel.pearsonprd.tech/courses/college-algebra/thumbnails/college-algebra

#FFFFFF

patrickJMT

Professor Dave Explains

Let's Tute

LearnZillion

Find the Common Difference for 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

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

Use the Permutations Formula

Counting Principles, Permutations, and Combinations

Find Particular Terms of a Sequence from the General Term

Use Recursion Formulas

Use Factorial Notation

Use Summation Notation

Sequences and Summation Notation

Understand the Principle of Mathematical Induction

Prove Statements Using Mathematical Induction

Mathematical Induction