AMC 12 Sequences, Series & Limits Flashcards
6 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 AMC 12 Sequences, Series & Limits flashcards as text
What is the sum of the arithmetic series 1 + 2 + 3 + … + 100?
Answer: 5050
The sum of the first n positive integers is n(n+1)/2 = 100·101/2 = 5050.
What is the common ratio of the geometric sequence 3, 6, 12, 24, …?
Answer: 2
Each term is twice the previous term, so the common ratio r = 6/3 = 2.
What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + …?
Answer: 2
For |r| < 1, the sum is a/(1 − r) = 1/(1 − 1/2) = 2.
In an arithmetic sequence with a₁ = 5 and common difference d = 3, what is a₁₀?
Answer: 32
aₙ = a₁ + (n − 1)d = 5 + 9·3 = 32.
What is the nth term of the geometric sequence 2, 6, 18, 54, …?
Answer: 2·3^(n−1)
With a₁ = 2 and r = 3, the nth term is a₁·r^(n−1) = 2·3^(n−1).
What is the sum of the first 5 terms of a geometric series with a₁ = 4 and r = 2?
Answer: 124
Sₙ = a₁(rⁿ − 1)/(r − 1) = 4(2⁵ − 1)/(2 − 1) = 4·31 = 124.
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