Sequences & 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 & Series flashcards as text
In the Fibonacci sequence 1,1,2,3,5,8,13,..., what is the 8th term?
Answer: 21
Listing the terms: 1,1,2,3,5,8,13,21 — the 8th term is 21.
What is the sum of k^2 for k=1 to 5?
Answer: 55
1+4+9+16+25=55.
What is the 7th term of a geometric sequence with first term 2 and ratio 3?
Answer: 1458
a_7=2*3^6=2*729=1458.
The formula for the sum of the first n perfect squares is:
Answer: n(n+1)(2n+1)/6
The closed-form formula for sum of first n squares is n(n+1)(2n+1)/6.
A ball dropped from 10m rebounds to 3/5 of the previous height each bounce. What is the total distance traveled?
Answer: 40
Total=10+2*(6/(1-3/5))=10+30=40 meters.
What is the coefficient of x^3 in the expansion of (1+x)^6?
Answer: 20
By the binomial theorem, the coefficient is C(6,3)=20.