Practice - Practice Problems
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Practice Questions
Test your understanding with targeted questions
Find the 6th term of the sequence: 2, 6, 18, 54,…
💡 Hint: Use the formula for the n-th term: T = ar^(n-1).
Is the sequence 1, 3, 9, 27 geometric? Justify.
💡 Hint: Check the ratio of consecutive terms.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the 4th term in a geometric sequence with a=2 and r=3?
💡 Hint: Use the n-th term formula.
An infinite geometric series converges only if the absolute value of the common ratio is less than 1.
💡 Hint: Remember the condition for convergence.
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Challenge Problems
Push your limits with advanced challenges
A company invests $100,000 in a project that appreciates in value by 8% per year. How much will it be worth in 15 years?
💡 Hint: Apply the compound interest formula.
You observe that the size of a certain bacteria population doubles every 4 hours. If you start with a population of 250 bacteria, how large will it be after 24 hours?
💡 Hint: Determine how many doubling periods there are in 24 hours.
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Reference links
Supplementary resources to enhance your learning experience.