Hello, my name is Todd and I need help with the problem : Express 5120 as a sum of more than 1 consecutive number.

It is supposed to be of middle school standard.

P.S. I am a student

Hi Todd,

Before we get into your problem, just a couple of preliminary things to think about.

What do "consecutive numbers" look like. Well, an example of 3 consecutive numbers is 1, 2, 3. Another example is 35, 36, 37. What is the same about these? Each time you add one to the first number to get the second number. The third number is then one more than the second, or another way to look at it is as two more than the first number. So the general form of consecutive numbers is n, n+1, n+2, n+3, .... and so on.

Now that we understand consecutive numbers, let's look at solving equations with one variable. For example, 3x + 5 = 26. Let's look at the steps to solving this kind of equation:

3x + 5 = 26     
3x + 5 - 5 = 26 - 5    subtract 5 from both sides
3x = 21     simplify
3x/3 = 21/3    divide by sides by the number in front of the x
x = 7    simplify and now we have the answer
We will use this type of solving equations in solving your problem.

You need to find consecutive numbers that add up to 5120 but you are not told now many consecutive numbers you need. Let's make a chart to keep track of our work. We will start by looking for 2 consecutive numbers. If we can't find any we will look for 3, then 4 and so on.

# of consecutive numbersWhat does it look like?Equation we need to solve:
2n + n+1 = 2n+15120 = 2n + 1

If the value we get for n is an integer (no decimals or fractions allowed), then we have found the first of the consecutive numbers. A quick check shows that for 2 consecutive numbers, there is no integer solution for n and we have to try the next choice, 3 consecutive numbers:

# of consecutive numbersWhat does it look like?Equation we need to solve:
3n + n+1 + n+2 = 3n+35120 = 3n + 3

I will let you finish the problem off. You should be able to get it from here.

Hope this helps,


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