Patterns and Sequences - GED Math

The series follows the pattern

.

Plug in the last number given:

The symbols show that if one number is equal to another, the equality holds no matter the order of the two. This is the symmetric property of equality.

The symbols express the idea that two numbers equal to the same number are also equal to each other. This is the transitive property of equality.

The symbols express the idea that any number is equal to itself. This is the reflexive property of equality.

The symbols express the idea that if a number is greater than a second number, which is greater than a third, then the first number is greater than the third. This is the transitive property of inequality.

The symbols express the idea that if three numbers are added, the same sum results regardless of which numbers are added first. This is the associative property of addition.

The sequence consists of the perfect square integer, except that every other element is negated. The sequence goes like this:

The next entry 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.

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.

We need to find ways to factor 28 such that the three factors are different, and then find the sum of those factors in each case.

28 can be expressed as the product of three integers four ways:

I)

II)

III)

IV)

We disregard (I) and (IV) since the factors are not distinct.

We look at (II) and (III):

II: Sum:

III: Sum:

Of the four choices, only 17 is a possible sum; that is the correct choice.

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:

Each term of the sequence is found by adding a number to the previous one; the number added is incremented by 2 each time, as seen below:

The next term, which is the missing term, is obtained by adding 12 to 26:

,

the correct choice.

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 .

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 .

Start by filling in the changes that happen from number to number in the sequence. This is done below in brackets:

Now, you know that

Thus, you know that the sequence will continue after by subtracting . Thus, the missing value is .

Notice that the numbers are increasing by 6 every time.

Add 6 to the end of the last number to obtain the number in the question mark.

The answer is:

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 .

Recall that in an arithmetic sequence, the difference between terms is constant. From the given first and second terms, we see that the sequence is increasing by for each term. Thus, the third term must be , and the fourth term must be .

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

The next entry:

,

the correct choice.