This is a sequence that features every other positive, odd integers.  The missing number in this case is 9.  

Find the next term in the following arithmetic series:

To find the next term in an arithmetic series, we need to find the common difference. To do so, find the difference between any two consecutive terms in the sequence:

Our common difference is 7. Now we need to add that to the last term to get what we want

So our next term is 32

What is the common difference of the following arithmetic series?

To find the common difference, we need to find the difference between any  two consecutive terms.

Try with the first two:

To be sure, try it with the 2nd and 3rd

We keep getting the same thing, -8. It must be negative, because our sequence is decreasing. Therefore, we have our answer: -8

The sequence is decreasing by 3 each term. To get from the first term to the 16th term, you must subtract 3 fifteen times:

Write the n-th term formula.

The  represents the first term, and  is the last term.  

The  is the common difference among the numbers.  

 since each term increases by two.

Solve for .

Divide by two on both sides.

The formula for n-terms in a arithmetic sequence is:

Substitute the known terms.

The answer is:  

Write the formula for the sum of an arithmetic series.

To determine the value of , use the formula:

Divide by five on both sides.

Substitute all the terms into the sum formula.

The answer is:  

Write the formula to determine the sum of an arithmetic series.

where  is the number of terms,  is the first term, and  is the last term.

Use the following formula to determine how many terms are in this series.

The term  is the common difference.  Since the numbers are spaced five units, .

Substitute the known values and solve for n.

Subtract two from both sides, and distribute the five through the binomial.

Add five on both sides.

Divide by five.

Plug this value and the other givens to the sum formula to determine the sum.

The answer is:  

This represents an arithmetic sequence.  Write the formula.  

Substitute the first term and the common difference in the formula.

Simplify the terms.

The answer is:  

Write the formula for the arithmetic sequence.

The first term is:  

The common difference is the same for each term, which is increasing by six every term:  

Substitute and simplify the formula.

To find the hundredth term, plug in .

The answer is:  

An arithmetic sequence is one in which each term is generated by adding the same number - the common difference - to the previous term. As can be seen here, the differences between each term and the previous term is not constant from term to term:

The sequence cannot be arithmetic.

A geometric sequence is one in which each term is generated by multiplying the previous term by the same number - the common ratio. As can be seen here, the ratio of each term to the previous one is the same:

The sequence could be geometric.