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 lim(n→∞) of (1 + 1/n)^n?
Answer: e
This is the classic definition of Euler's number: lim(n→∞)(1 + 1/n)^n = e ≈ 2.718.
What is the sum of the infinite geometric series with a₁ = 9 and r = 1/3?
Answer: 13.5
S∞ = a₁/(1 − r) = 9/(1 − 1/3) = 9/(2/3) = 27/2 = 13.5.
The series 1 − 1 + 1 − 1 + … is best described as:
Answer: divergent
The partial sums oscillate between 0 and 1 without approaching a fixed value, so the series diverges.
What is the arithmetic mean of the sequence 4, 8, 12, 16, 20?
Answer: 12
Mean = (4 + 8 + 12 + 16 + 20)/5 = 60/5 = 12.
What is the value of Σ(k=1 to ∞) of (1/2)^k?
Answer: 1
This geometric series has first term a = 1/2 and ratio r = 1/2, so S = (1/2)/(1 − 1/2) = 1.
A sequence is defined by aₙ = 3aₙ₋₁ − 2 with a₁ = 5. What is a₃?
Answer: 37
a₂ = 3(5) − 2 = 13 and a₃ = 3(13) − 2 = 37.
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