Question

to make a number pattern, yuan used the rule add 5, with a whole number as the starting point. which statement must be true about yuans list of numbers? each number is a multiple of 5. it has an even number that is prime. the numbers alternate between even and odd. none of these statements must be true.

Explanation:

Step1: Analyze multiples of 5

If the starting - point is not a multiple of 5, adding 5 repeatedly will not result in all numbers being multiples of 5. For example, if the starting number is 1, the sequence is 1, 6, 11, etc., which are not multiples of 5.

Step2: Analyze the even - prime number

The only even prime number is 2. There is no guarantee that 2 will be in the sequence. For example, if the starting number is 3, the sequence is 3, 8, 13, etc., and 2 is not in it.

Step3: Analyze even - odd alternation

Since 5 is an odd number, when we start with a whole number \(n\) and keep adding 5:
If \(n\) is even (\(n = 2k\) for some integer \(k\)), then \(n+5=2k + 5\) is odd. If \(n\) is odd (\(n=2k + 1\) for some integer \(k\)), then \(n + 5=(2k + 1)+5=2k+6 = 2(k + 3)\) is even. So the numbers alternate between even and odd.

Answer:

The numbers alternate between even and odd.