Question

Which of the following can not be expressed as the sum of three consecutive integers? a. 8922 b. 3852 c. 2523 d. 4663

Answer 1

Answer:

d)4663

Step-by-step explanation:

because it is not divide by 3

Answer 2

Answer:

Option (d) 4663 not be expressed as the sum of three consecutive integers.

Step-by-step explanation:

Given:

a. 8922 b. 3852 c. 2523 d. 4663

To find:

Not be expressed as the sum of three consecutive integers.

Any three consecutive integers include exactly one integer that is a multiple of 3.

Consider the three possibilities for which one is the multiple of 3 . To make it easier to think about, call the one that is a multiple of 3n.

Case 1: n is the smallest of the three.

Then the sum is n+(n+1)+(n+2) = n+n+1+n+2 = 3n+3 = 3(n+1).

This is a multiple of 3.

Case 2: n is the middle one of the three.

Then the sum is (n-1)+n+(n+1)=n-1+n+n+1=3 n.

This is a multiple of 3.

Case 3: n is the largest of the three.

Then the sum is (n-2)+(n-1)+n = n-2+n-1+n = 3n-3 = 3(n-1).

This is a multiple of 3.

In all three cases, the sum is a multiple of 3.

Using the above following cases, the sum of 4663 not be expressed as the sum of three consecutive integers.

Therefore, the correct answer is option d). 4663

#SPJ3