Classify each of the following statements as true or false. a. The sum of every

Question

Classify each of the following statements as true or false. a. The sum of every three consecutive numbers is divisible by 3. b. The sum of every four consecutive numbers is divisible by 4. a. Choose the correct answer below. A. The statement is true Every group of three consecutive numbers can be manipulated so that resulting numbers used in the sum are each divisible by thus, their sum is divisible by 3. B. The statement is true. A number will always divide a sum of the round using that number of items. C. The statement is false. The sum of every three consecutive numbers is divisible by 2. D. The statement is false. The number is a result of a sum, so it cannot be divisible by 3. b. Choose the correct answer below. A. The statement is true. The sum can be rearranged into the sum of even numbers. Because both numbers are divisible by 2, their sum is divisible by 4. B. The statement is false. There are two even numbers and two odd numbers, so the sum is divisible by 2, but is not always divisible by 4. C. The statement is false. The sum of will only be divisible by 4, if it is the result of four odd numbers, because that is not always the case, the statement is not true. D. The statement is true. A number will always divide a sum, if the sum is found using that number of terms.

Explanation / Answer

Let the number are a, a+ d and a + 2d

Sun is 3a + 3d = 3(a+d)

So sum is divisible by 3

True

b)

Let's the number is a , a+d , a+ 2d and a+3d

So sum of four consecutive number is 4a + 6d = 2(2a+3d)

So sum is not divisible by 4

False.

You can verify the above results by taking any consecutive values.

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