Algebra 1 : How to find consecutive integers

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : Quadratic Formula

The product of two consective positive odd integers is 143. Find both integers.

Possible Answers:

Correct answer:


If  is one odd number, then the next odd number is . If their product is 143, then the following equation is true.

Distribute into the parenthesis.

Subtract 143 from both sides.

This can be solved by factoring, or by the quadratic equation. We will use the latter.

We are told that both integers are positive, so .

The other integer is .

Example Question #1 : Arithmetic Series

Write a rule for the following arithmetic sequence:

Possible Answers:

Correct answer:


Know that the general rule for an arithmetic sequence is


where  represents the first number in the sequence,  is the common difference between consecutive numbers, and  is the -th number in the sequence.  

In our problem, .

Each time we move up from one number to the next, the sequence increases by 3.  Therefore,

The rule for this sequence is therefore .

Example Question #41 : Sequences

If the rule of some particular sequence is written as


find the first five terms of this sequence

Possible Answers:

none of these

Correct answer:


The first term for the sequence is where . Thus,

So the first term is 4.  Repeat the same thing for the second , third , fourth , and fifth  terms.

We see that the first five terms in the sequence are

Example Question #42 : Sequences

What are three consecutive numbers that are equal to ?

Possible Answers:

Correct answer:


When finding consecutive numbers assign the first number a variable.

If the first number is assigned the letter n, then the second number that is consecutive must be  and the third number must be .

Write it out as an equation and it should look like:

Simplify the equation then,


If  then 


So the answer is 

Example Question #43 : Sequences

The sum of five odd consecutive numbers add to . What is the fourth largest number?

Possible Answers:

Correct answer:


Let the first number be .

If  is an odd number, the next odd numbers will be:

, and 

The fourth highest number would then be:

Set up an equation where the sum of all these numbers add up to .

Simplify this equation.

Subtract 20 from both sides.

Simplify both sides.

Divide by five on both sides.

Corresponding to the five numbers, the set of five consecutive numbers that add up to  are: 

The fourth largest number would be .

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