Arithmetic Sequences and Series

Dive into the world of arithmetic sequences and series with this comprehensive tutorial! We'll tackle 9 practice problems together, covering everything from identifying common differences and writing explicit and recursive formulas to calculating partial sums and working with Sigma notation.

Whether you're just starting with sequences or need a refresher on series, this video will guide you through the essential concepts. Learn how to find any term in a sequence, calculate the sum of a given number of terms, and solve word problems involving arithmetic series.

In this video, you'll learn:

What an arithmetic sequence is and how to find the common difference (d).
Understanding sequence notation (a sub n, a sub 1).
How to write an explicit formula for an arithmetic sequence (a sub n = a sub 1 + (n-1)d).
How to write a recursive formula for an arithmetic sequence.
Finding specific terms in a sequence using explicit formulas.
Calculating the sum of an arithmetic series (partial sums).
Using the sum formula (S sub n = n/2 * (a sub 1 + a sub n)).
Interpreting and solving problems with Sigma (summation) notation.
Solving word problems that involve finding missing elements of an arithmetic series.
Timestamps:

0:00 Introduction to Arithmetic Sequences and Series
0:20 What is an Arithmetic Sequence? (Common Difference 'd')
0:50 Sequence Notation Explained (a sub n, a sub 1)
1:20 Problem 1: Writing an Explicit Formula & Finding the 20th Term
2:40 Problem 1: Writing a Recursive Formula
4:30 Problem 2: Explicit, Recursive Formulas & Next Three Terms
6:50 Problem 3: Writing the First Five Terms from a Recursive Formula
7:50 Problem 4: Writing an Explicit Rule Given Two Terms (a sub 4, a sub 7)
10:40 Problem 5: Finding the Sum of the First 100 Integers (Series Introduction)
12:20 Problem 6: Finding the 15th Partial Sum of an Arithmetic Series
14:30 Problem 7: Summation Notation (Sigma Notation) Explained
16:40 Problem 8: Solving Another Sigma Notation Problem
18:30 Problem 9: Word Problem - Finding the First Term of an Arithmetic Series
22:00 Conclusion & Next Steps (Geometric Sequences & Series)
Perfect for Algebra 1, Algebra 2, and College Algebra students! Like this video, subscribe to Mario's Math Tutoring for more math lessons, and check out my video courses for deeper learning!

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