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
What is the 10th term of the arithmetic sequence 3, 7, 11, 15, ...?
Answer: 39
The common difference is 4, so a₁₀ = 3 + 9 × 4 = 3 + 36 = 39.
What is the sum of the first 100 positive integers?
Answer: 5050
Sum = n(n+1)/2 = 100 × 101/2 = 5050, as computed by Gauss.
A geometric sequence has first term 2 and common ratio 3. What is the 5th term?
Answer: 162
a₅ = a₁ × r^(n−1) = 2 × 3⁴ = 2 × 81 = 162.
What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ...?
Answer: 2
S∞ = a/(1−r) = 1/(1−1/2) = 2.
In the Fibonacci sequence 1, 1, 2, 3, 5, 8, ..., what is the 8th term?
Answer: 21
Continuing the Fibonacci sequence: the 8th term is 21.
The sum of the first n terms is Sₙ = 2n² + 3n. What is the first term a₁?
Answer: 5
a₁ = S₁ = 2(1)² + 3(1) = 5.