Question 14
A continuous look-and-say sequence is formed this way: Start with three 1’s;
read the terms as “three 1’s” and write down what you read as “31” at the end of
the sequence; read the next group of unread identical numbers as “one 3” and
write “13” at the end; continue this process to get an infinite sequence 1, 1, 1, 3,
1, 1, 3, 2, 1, ….
(a) What is the largest possible digit you could write down? Why? (5 points)
(b) What is the 20th term of this sequence? Why? (5 points)
(c) Will the number “333” appear in the sequence? Why or why not? (10 points)
(b) The 20th term of this sequence is . The reason is:
(c) □ Yes. □ No. The reason is:
read the terms as “three 1’s” and write down what you read as “31” at the end of
the sequence; read the next group of unread identical numbers as “one 3” and
write “13” at the end; continue this process to get an infinite sequence 1, 1, 1, 3,
1, 1, 3, 2, 1, ….
(a) What is the largest possible digit you could write down? Why? (5 points)
(b) What is the 20th term of this sequence? Why? (5 points)
(c) Will the number “333” appear in the sequence? Why or why not? (10 points)
(b) The 20th term of this sequence is . The reason is:
(c) □ Yes. □ No. The reason is: