# Consecutive Integer Problem Solver

#### Free Online Tool Solves Any Consecutive Integer Math Problem

A consecutive integer problem gives you the sum, product, or another function of a certain number of consecutive integers. Some variations also use consecutive even numbers or consecutive odd numbers.

Given the value of the function, the number of integers, and the fact that they are consecutive, you have enough information to solve the problem. You can find the solution by hand, or use the calculator below.

### Try the Consecutive Integer Problem Solving Calculator:

### Example Problem 1

The product of 7 consecutive odd integers is 760543875. What are the integers? To set up this math problem for solving, we can call the smallest integer*n*. The the equation we must solve is

*n*(

*n*+2)(

*n*+4)(

*n*+6)(

*n*+8)(

*n*+10)(

*n*+12) = 760543875

Notice that this is a seventh degree polynomial, which can only be solved by graphing or with numerical methods. Using the calculator above, we find that the integers are 13, 15, 17, 19, 21, 23, and 25.

### Example Problem 2

The sum of the cubes of 6 consecutive integers is 207675. As before, let's denote the smallest integer by*n*. Then the equation to solve is

*n*³ + (

*n*+1)³ + (

*n*+2)³ + (

*n*+3)³ + (

*n*+4)³ + (

*n*+5)³ = 207675

This simplifies to the cubic equation

6

*n*³ + 45

*n*² + 165

*n*+ 225 = 207675

You can use the cubic equation solver to find the value of

*n*, which is 30, or use the calculator above to produce all 6 numbers: 30, 31, 32, 33, 34, and 35.

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