# GED Math : Patterns and Sequences

## Example Questions

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### Example Question #21 : Patterns And Sequences

Give the next number in the sequence:

Explanation:

To generate the sequence, begin with 4, then alternately multiply by 3 and add 2:

The next entry:

,

the correct choice.

### Example Question #22 : Patterns And Sequences

Find the missing number in the sequence:

Explanation:

Find the missing number in the sequence:

We have a sequence where each term is a multiple of the previous term. This is known as a geometric series.

We need to find the common multiple, and then use it to find our second term. To find the common multiple, divide any term by its previous term.

ex)

So, our common multiple is 7. Use this to find our second term.

### Example Question #23 : Patterns And Sequences

Find the missing term in the following arithmetic series:

Explanation:

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:

### Example Question #181 : Numbers

The first term of an arithmetic sequence is . If the second term is , and the third term is , what is the tenth term of the sequence?

Explanation:

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 .

### Example Question #25 : Patterns And Sequences

If the first three terms of an arithmetic sequence are 5, 12, and 19, what is the fifth term of the sequence?