Change in Arithmetic and Geometric Sequences
Alice White
6 min read
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Study Guide Overview
This study guide covers arithmetic and geometric sequences. Key concepts include defining sequences, identifying the common difference (d) in arithmetic sequences and the common ratio (r) in geometric sequences. It also provides formulas for finding the nth term of both types of sequences and explains the difference between change and rate of change. Practice questions are included.
#AP Pre-Calculus: Sequences - Your Night-Before Review 🚀
Hey there! Let's get you prepped for your AP Pre-Calculus exam with a quick, focused review of sequences. We'll break down arithmetic and geometric sequences, highlighting key formulas and concepts to make sure you're feeling confident. Let's do this!
#2.1 Change in Arithmetic and Geometric Sequences
#What is a Sequence? 🤔
A sequence is essentially a function that maps whole numbers to real numbers. Think of it as an ordered list of numbers, where each number has a specific position. The graph of a sequence consists of discrete points, not a continuous curve, because we're only dealing with whole numbers as inputs.
For example, if you track your daily steps, each day (1st, 2nd, 3rd, etc.) corresponds to a specific number of steps. These points are plotted separately, not connected by a line. 🚶♀️
#Arithmetic Sequences ➕
An arithmetic sequence is a sequence where the difference between any two consecutive terms is constant. This constant difference is called the common difference, denoted by d. It's like adding the same number each time to get the next term. 💡
- Constant Rate of Change: The terms in an arithmetic sequence increase or decrease at a constant rate, which is equal to the common difference.
- Example: 2, 5, 8, 11, 14... (Here, d = 3).
#Formula and Example 😎
The nth term of an...
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