AMC12 Sequences & Series 2

Question 1

In the Fibonacci sequence 1,1,2,3,5,8,13,..., what is the 8th term?

Accepted Answer

21

Answer

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?

Accepted Answer

55

Answer

1+4+9+16+25=55.

Question 3

What is the 7th term of a geometric sequence with first term 2 and ratio 3?

Accepted Answer

1458

Answer

a_7=2*3^6=2*729=1458.

Question 4

The formula for the sum of the first n perfect squares is:

Accepted Answer

n(n+1)(2n+1)/6

Answer

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?

Accepted Answer

40

Answer

Total=10+2*(6/(1-3/5))=10+30=40 meters.

AMC12 - American Mathematics Competition 12 Practice Test