Question

Put the following statements into order to prove that is divisible by 3 for all non-negative integers n. Put N next to the statements that should not be used.

Answer 1

N  2   3   N  N   5   4   N   N   1   next to the statements that should not be used.

What is sequence and example?

• A sequence is an ordered list of numbers . The three dots mean to continue forward in the pattern established.
• Each number in the sequence is called a term. In the sequence 1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on.

sequence

• The statement is true for n = 0 because 0 is divisible by 3.
• Now suppose we have proved the statement for some n element of N This means that 4^n -1 = 3k for some integer k..
• We now consider the quantity 4^n+1 -1 = 4 . 4^n - 1 = 3 . 4^n + 4^n - 1
• We use the inductive hypothesis to simplify that equation to 4^n+1 - 1 = 3 . 4^n + 3k = 3 (4^n + k).
• We have thus shown that 4^n+ 1- 1 is a multiple of 3.

Learn more about sequence

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