1 Solve each of the following two problems You may use this

1. Solve each of the following two problems. You may use this word document to write your answers after each question. Examine these number patterns: 15 = 7 + 8 15 = 4 + 5 + 6 10 = 1 + 2 + 3 + 4 9 = 4 + 5 9 = 2 + 3 + 4 a) What kind of numbers can be written as a sum of 2, or 3, or 4 consecutive numbers? Give examples to verify your response.

Solution

2 numbers : Numbers are n and n + 1

Add them up ---> 2n+ 1, which is an odd value

So, when we add 2 consecutive numbers, we get an ODD value ALWAYS

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3 numbers :

Let the numbers be n-1, n and n+1

When we add them up, n-1 + n + n+1 ----> 3n

which is ALWAYS a multiple of 3

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4 numbers :

n+1,n+2,n+3 and n+4

This is 4n + 10

As in, 2(2n + 5) , which is an EVEN number