Question

A sequence of numbers starts with $1,$ $2,$ and $3.$ The fourth number of the sequence is the sum of the previous three numbers in the sequence: $1 + 2 + 3 = 6.$ In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence?

$11$

$20$

$37$

$68$

$99$

Answer: D

Concepts:recursion

Difficulty rating: 770

Solution:

The sequence begins $1,2,3$ .

The next terms are $1+2+3=6$ , $2+3+6=11$ , $3+6+11=20$ , $6+11+20=37$ , and $11+20+37=68$ .

Thus, D is the correct answer.

2009 AMC 8 Problem 5

Answer: D

Difficulty rating: 770

Solution:

Problem 5 in Other Years