The common difference is the distance between each number in the sequence. Notice that each number is 3 away from the previous number.

What is the common difference in the following sequence?

Common differences are associated with arithematic sequences. 

A common difference is the difference between consecutive numbers in an arithematic sequence. To find it, simply subtract the first term from the second term, or the second from the third, or so on...

See how each time we are adding 8 to get to the next term? This means our common difference is 8.

The common difference in this set is the linear amount spaced between each number in the set.

Subtract the first number from the second number.

Check this number by subtracting the second number from the third number.

Each spacing, or common difference is:  

The common difference can be determined by subtracting the first term with the second term, second term with the third term, and so forth.   The common difference must be similar between each term.

The distance between the first and second term is .

The distance between the second and third term is .

The distance between the third and fourth term is .

The fractions may seem as though they have a common difference since the denominators are increasing by one for each term, but there is no common difference among the numbers.

The answer is:  

In order to determine the common difference, subtract the first term from the second term.

Verify that this is the same for the difference of the third and second terms.

The set of data is increasing at increments of five.  

The common difference is:  

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 .

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 .

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

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 

And 

So the answer is 

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 .