AMC12 Sequences and Series 2

Question 1

Which term of the arithmetic sequence 4, 7, 10, 13, ... is equal to 100?

Accepted Answer

33rd

Answer

4 + (n−1) × 3 = 100 gives 3(n−1) = 96, so n = 33.

Question 2

A ball is dropped from 16 feet and bounces to 3/4 of its height each time. What is the total distance traveled?

Accepted Answer

112 ft

Answer

Total = 16 + 2 × (12)/(1/4) = 16 + 96 = 112 feet.

Question 3

What is ∑(k=1 to 5) k²?

Accepted Answer

55

Answer

1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55.

Question 4

A sequence has aₙ = 2n − 1. What is a₁ + a₂ + ... + a₁₀?

Accepted Answer

100

Answer

This is the sum of the first 10 odd numbers, which equals 10² = 100.

Question 5

In a geometric series with a₁ = 1 and r = 2, what is a₄?

Accepted Answer

8

Answer

a₄ = a₁ × r³ = 1 × 2³ = 8.

AMC12 - American Mathematics Competition 12 Practice Test