To pattern uses the formula .

Understanding this sequence takes a quick eye, so to speak. Notice this interesting fact. You can rewrite the sequence as follows:

That is a rather simple sequence if you think of it. The best clue to help you see it will likely be the transition between and . These are the numbers that will most like stand out as a square and a cube. Based on this data, you can reasonably guess that the next number in the sequence is or .

Recall that in an arithmetic sequence, we will be adding or subtracting the same number to get each successive term.

We can tell that the terms are decreasing by each time. Thus, we can make a table to figure out the tenth term.

The tenth term is .

Add 2 to the first number to get the second; each subsequent increment is increased by 2. The pattern:

Add 12 to get the next element:

, which is the correct choice.

The pattern of the sequence is .

Therefore,

Recall that in an arithmetic sequence, you will be adding or subtracting by a certain number to get the subsequent values in the sequence.

From the given numbers, you should notice that the sequence is increasing by every time. Thus, the fourth number in the sequence should be . The fifth number in the sequence must be .

Begin by considering how much the numbers change between each set of values. The following places the change in brackets:

You can guess that the next change will be by . Therefore, the next value in the sequence will be or .

After the first two elements, each subsequent element is the sum of the previous two (similar to the Fibonacci sequence).

The third and subsequent elements are calculated as follows:

, the correct response.

The numbers can be seen as increasing by four per term since:

This means the term after three is four more than three.

The answer is:

Find the missing term in the following arithmetic series:

An arithmetic series is one in which the next term is found by adding a constant number to the previous term. This is called the common difference.

First, we need to find the common difference. Do so by subtracting any term from its following term.

Note that it doesn't matter which pair of consecutive terms we choose, just so long as we subtract the smaller from the larger.

So, our common difference is 13. Thus, our answer can be found via the following:

So our answer is 44