Question

use inductive reasoning to predict the next line in the pattern.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

the next line in the pattern is \\(\square, \square, \square, \square, \square, \square\\).
(type whole numbers.)

Explanation:

Step1: Identify pattern rule

Each inner term is the sum of the two terms directly above it; the first and last terms of each line are always 1.

Step2: Calculate new inner terms

• Second term: $1 + 4 = 5$
• Third term: $4 + 6 = 10$
• Fourth term: $6 + 4 = 10$
• Fifth term: $4 + 1 = 5$

Step3: Construct full line

Start and end with 1, then insert the calculated inner terms in order.

Answer:

1, 5, 10, 10, 5, 1