Sequences and Series Flashcards

6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Sequences and Series flashcards as text

Which term of the arithmetic sequence 4, 7, 10, 13, ... is equal to 100?
Answer: 33rd
4 + (n−1) × 3 = 100 gives 3(n−1) = 96, so n = 33.
A ball is dropped from 16 feet and bounces to 3/4 of its height each time. What is the total distance traveled?
Answer: 112 ft
Total = 16 + 2 × (12)/(1/4) = 16 + 96 = 112 feet.
What is ∑(k=1 to 5) k²?
Answer: 55
1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55.
A sequence has aₙ = 2n − 1. What is a₁ + a₂ + ... + a₁₀?
Answer: 100
This is the sum of the first 10 odd numbers, which equals 10² = 100.
In a geometric series with a₁ = 1 and r = 2, what is a₄?
Answer: 8
a₄ = a₁ × r³ = 1 × 2³ = 8.
What is the arithmetic mean of 2, 5, 8, 11, 14?
Answer: 8
The sum is 40, divided by 5 gives mean = 8; it also equals the middle term of this AP.