Geometric Sequences: Finding the nth Term
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Objective
Students are learning how to write the general term of a geometric sequence, find the value of the nth term, and understand growth and decay in geometric patterns.
Part 1 of 4
Warm-up video
Khan Academy · 10:45Vetted channel
We don't generate video — this one is by Khan Academy on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.
Part 2 of 4
Key concepts
3 concepts
- 1
A geometric sequence is a sequence where each number is found by multiplying the previous number by a fixed value called the common ratio.
- 2
If the first term (a₁) of a geometric sequence is 90 and the common ratio is -⅓, the second term is -30 and the third term is 10.
- 3
In a bungee jumping scenario where the initial jump stretches 120 feet and each bounce is 60% of the previous stretch, the stretch on the nth bounce can be calculated as 120 * 0.6ⁿ.
Part 3 of 4
Practice
7 questions
What is a geometric sequence? Explain in your own words how it differs from a regular sequence.
Anne goes bungee jumping off of a bridge above water. On the initial jump, the cord stretches by 120 feet. On the next bounce, the stretch is 60% of the original jump, and then each additional bounce stretches the rope 60% of the previous stretch. Write a formula to represent the stretch on the nth bounce.
Part 4 of 4
Exit ticket
Quick comprehension check
“The first term of a geometric sequence is 5, and the common ratio is 2. What are the first four terms of this sequence?”
Sample answer included in the free materials
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