Sequences and Series Flashcards

6 cards from real AIME 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

Find the 10th term of the arithmetic sequence 3, 7, 11, 15, …
Answer: 39
a_n=3+(n-1)×4; a_10=3+36=39.
What is the sum of the first 20 terms of the arithmetic sequence 2, 5, 8, 11, …?
Answer: 610
S_20=20/2×(2·2+19·3)=10×(4+57)=10×61=610.
Find the common ratio of the geometric sequence 3, 6, 12, 24, …
Answer: 2
Each term is doubled: ratio = 6/3 = 2.
Find the 6th term of the geometric sequence 2, 6, 18, …
Answer: 486
a_6=2×3^5=2×243=486.
What is the sum of the infinite geometric series 4 + 2 + 1 + 1/2 + …?
Answer: 8
S=a/(1-r)=4/(1-1/2)=4/(1/2)=8.
An arithmetic sequence has first term 5 and common difference -3. Find the sum of the first 10 terms.
Answer: -85
S_10=(10/2)(2×5+9×(-3))=5(10-27)=5(-17)=-85.