AMC12 Sequences & Series 2 — Questions and Answers
Question 1: In the Fibonacci sequence 1,1,2,3,5,8,13,..., what is the 8th term?
- 13
- 34
- 8
- 21 (Correct answer)
Correct answer: 21
Listing the terms: 1,1,2,3,5,8,13,21 — the 8th term is 21.
Question 2: What is the sum of k^2 for k=1 to 5?
- 25
- 30
- 45
- 55 (Correct answer)
Correct answer: 55
1+4+9+16+25=55.
Question 3: What is the 7th term of a geometric sequence with first term 2 and ratio 3?
- 729
- 2187
- 486
- 1458 (Correct answer)
Correct answer: 1458
a_7=2*3^6=2*729=1458.
Question 4: The formula for the sum of the first n perfect squares is:
- n(n+1)/2
- n^2(n+1)^2/4
- n(2n+1)/3
- n(n+1)(2n+1)/6 (Correct answer)
Correct answer: n(n+1)(2n+1)/6
The closed-form formula for sum of first n squares is n(n+1)(2n+1)/6.
Question 5: A ball dropped from 10m rebounds to 3/5 of the previous height each bounce. What is the total distance traveled?
- 25
- 50
- 35
- 40 (Correct answer)
Correct answer: 40
Total=10+2*(6/(1-3/5))=10+30=40 meters.
Question 6: What is the coefficient of x^3 in the expansion of (1+x)^6?
- 15
- 6
- 10
- 20 (Correct answer)
Correct answer: 20
By the binomial theorem, the coefficient is C(6,3)=20.
AMC12 Sequences & Series 2
In the Fibonacci sequence 1,1,2,3,5,8,13,..., what is the 8th term?