AMC8 2009
AMC8 2009 · Q5
AMC8 2009 · Q5. It mainly tests Sequences & recursion (algebra).
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?
一个数字序列以1、2和3开始。序列的第四个数字是前三个数字的和：$1 + 2 + 3 = 6$。同样，第四个之后的每个数字都是前三个数字的和。序列的第八个数字是多少？
(A)
11
11
(B)
20
20
(C)
37
37
(D)
68
68
(E)
99
99
Answer
Correct choice: (D)
正确答案：（D）
Solution
Make the list like the picture:
So the eighth number in the sequence is 68.
列出序列，如何所示：
所以序列的第八个数字是68。
Topics
Related Questions
Practice full AMC exams on amcdrill.
Try full-length practice and diagnostics at www.amcdrill.com.