Recap: Geometric Sequences

Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 41 of 46.

Challenge

The sequence 80, 40, 20, ... has the rule $a\left(n\right) = 80\cdot {\frac{1}{2}}^{n-1}$ . Work out $a\left(5\right)$ . Tap the move that uses the rule, then type the arithmetic line by line.

Try it yourself

a\cdot 5

Simplify

Given $a\left(n\right) = 80\cdot \frac{1}{2}^{n-1}$

All lessons in Exponentials, Logs & Sequences

1Exponential Functions

Repeated Multiplying Drawing Growth Doubling Drawing Decay

4Meet the Logarithm

What a Log Is Reading a Log Logs of Fractions From Log to Power Recap: Logarithms

7Log Equations

Combine, Then Undo A Difference of Logs Same Log Both Sides A False Answer Recap: Log Equations

10Final Challenges

Final: Same Base Final: Log It Final: Two Logs Final: The Investment Final: The Staircase

2Growth and Decay

Growing by a Percent How Long Until?Recap: Growth and Decay

5Log Rules

The Product Rule The Quotient Rule The Power Rule Into One Log Recap: Log Rules

8Arithmetic Sequences

The nth Term Which Term?Adding the Terms Recap: Arithmetic Sequences

3Same-Base Equations

Matching Powers Rewriting the Base An Expression Upstairs Fractions and Negatives Recap: Same Base

6Solving with Logs

Take the Log Isolate the Power First Base e Undoing ln Recap: Solving with Logs

9Geometric Sequences

Multiply Each Time Finding the Ratio Geometric Sums Forever SumsRecap: Geometric Sequences