Recursively Defined Sequences - Arithmetic and Geometric Sequences

Overview

Learn about recursively defined sequences in this comprehensive mathematics lecture and problem-solving session. Master the concept of recursive functions, which use previous terms to generate subsequent values in a sequence, contrasting them with explicit rules that rely on term position. Explore arithmetic sequences with their f(n) = f(n - 1) + d formula and geometric sequences using f(n) = r*f(n - 1), understanding how to determine first terms and common differences/ratios. Dive into special sequences like the Fibonacci sequence, where terms are generated using multiple previous values. Work through 59 carefully structured practice problems, with timestamps provided for easy navigation through different problem sets. Access downloadable resources including textbook materials and scaled graph paper to enhance your learning experience. Perfect for students seeking to strengthen their understanding of sequence patterns, recursive formulas, and their practical applications in mathematics.

Syllabus

Introduction
Lecture overview
Problem #1-2
Problem #3-6
Problem #7-12
Problem #13-20
Problem #21-22
Problem #23-28
Problem #29-34
Problem #35-38
Problem #39-44
Problem #45-46
Problem #47-51
Problem #52
Problem #53
Problem #54
Problem #55
Problem #56
Problem #57
Problem #58
Problem #59