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Applied Linear Equations: Consecutive Numbers - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

In Algebra II, we sometimes see consecutive number problems. Consecutive number problems may ask us to find a sum of integers or the specific integers themselves. To solve these problems, we set up a linear equation or a system of linear equations and then solve for a variable. These types of problems are often found on the SAT and ACT.

So consecutive number problems are in other way that linear equations come up. And consecutive number problems are just problems that involve numbers that are in a row so if you're dealing with like 3, 4, 5, 6 something of that nature where they're just numbers back to back to back. For this particular example we're dealing with four consecutive numbers such that the sum of the last three is four times the first. Okay so let's go take a look at sort of how we can represent consecutive numbers.
Okay so let's call the first number just x, okay the next number is just going to be the one following that. So if we started with the number 5 the next number would be 6 we just add one to the previous. So that means our second number is just x+1, to get our third same exact pattern just add another one to our second or to from our first that leaves our fourth and as you guessed it x+3.
Okay for this particular example we're summing the last three and having it be four times the first. So we basically want to sum our last three numbers, so that mean we want to add those last three numbers ad it's going to be four times the first. Now the trick is which is going to be bigger? These three added together or the first it says the sum is four times the first. So this sum is actually four times bigger which means we have to throw the four next to that first number. So here we added the second, third and fourth and together, that is going to be four times our first number. You know how that equation we can solve combining like terms over here we have x, x and x. So this becomes 3x adding 1, 2 and 3 becomes 6=4x. Get all our x's to one side subtract that 3x over we end up with x is equal to 6 okay.
As always with word problems make sure you're answering the right question so let's find four consecutive numbers so we want to give our four numbers. We found x which we actually found as the first, so our first number is 6 second is 7, 8 and 9. So taking our equation, taking our word problem turning in to equation solving it out you're able to find the consecutive numbers.

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