Sequences & Series Flashcards
6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning โ missed cards come back until you master them.
Read the first 6 Sequences & Series flashcards as text
If a_n = 2n-1, what is the sum of the first 10 terms?
Answer: 100
The first 10 odd numbers sum to 10^2=100.
What is the sum from k=1 to 100 of (1/k - 1/(k+1))?
Answer: 100/101
This telescoping series sums to 1-1/101=100/101.
In a geometric sequence the 3rd term is 18 and the 6th term is 486. What is the common ratio?
Answer: 3
r^3=486/18=27, so r=3.
What is the sum of the arithmetic series 5 + 8 + 11 + ... + 50?
Answer: 440
There are (50-5)/3+1=16 terms; sum=16*(5+50)/2=8*55=440.
What is the sum from k=1 to 10 of (2k-5)?
Answer: 60
Sum=2*sum(k)-5*10=2*55-50=110-50=60.
An infinite geometric series has sum 12 and first term 3. What is the common ratio?
Answer: 3/4
3/(1-r)=12 gives 1-r=1/4, so r=3/4.