The set of whole numbers comprises the following:

\(\displaystyle \left \{ 0, 1, 2, 3, 4, 5...\right \}\)

All of the given choices are members of this set.

Each entry in the sequence is obtained by adding to the previous entry a number that increases by 1 each time.

\(\displaystyle 2 + 2 = 4\)

\(\displaystyle 4+3 = 7\)

\(\displaystyle 7+4=11\)

\(\displaystyle 11+5=16\)

\(\displaystyle 16+6=22\)

To get the next entry, add 7.

\(\displaystyle 22+7= 29\)

The set is increasing. To figure out by how much, simply subtract any two numbers in the set, but remember to put the greater number first!

Example: \(\displaystyle 2.3 -1.2 =1.1\)

Each number in the set increases by 1.1. To find the missing part of this set, add 1.1 to the number just before the blank.

\(\displaystyle 1.1 +3.4 = 4.5\)

The complete set is: 1.2, 2.3, 3.4, 4.5, 5.6.

First, you must notice that the set is increasing. When you look at how all the numbers are related, you will notice that this is a “growing” set, meaning the difference between each number in the set is increasing. To figure out by how much, simply subtract any two numbers in the set.

When you subtract the first two numbers in the set, you will get: \(\displaystyle 7-6=1\).

If you subtract the next two numbers, you will get: \(\displaystyle 9-7=2\).

Then the next two: \(\displaystyle 10-7=3\).

Now you can see a pattern. Each number increases by 1, 2, 3, and so on.

\(\displaystyle 6(+1),\ 7(+2),\ 9(+3),\ 12(+4),\ 16(+5),\ 21(+6),\ ?,\ 34\)

To find the missing number in the set, we must add 6 to 21.

\(\displaystyle 21+6=27\)

Now we can see the complete set.

\(\displaystyle 6(+1),\ 7(+2),\ 9(+3),\ 12(+4),\ 16(+5),\ 21(+6),\ 27(+7),\ 34\)

First, you must notice that the set is counting up/forwards. When you look at how all the numbers are related, you will notice that these numbers increase by 9, or are multiples of 9. To solve you can add 9 to the last known number and then 9 to the next:

 \(\displaystyle 54+9=63\)

\(\displaystyle 63+9=72\)

Or you can count by 9 to fill in the missing numbers.  The complete set is: 27, 36, 45, 54, 63, 72, 81.

In the number sequence \(\displaystyle 2, 8, 4, 16, 8, 32, 16 ...\), the first number is multiplied by \(\displaystyle 4\) to get the second number. The second number is divided by \(\displaystyle 2\) to get the third number. Numbers are then alternately multiplied by \(\displaystyle 4\) and divided by \(\displaystyle 2\) as the sequence continues.

Since \(\displaystyle 32\) is divided by \(\displaystyle 2\) to get \(\displaystyle 16\) at the end of the given numbers, the next step is to multiply by \(\displaystyle 4\). This gives the number \(\displaystyle 64\) as the next in the sequence. The pattern is to divide by \(\displaystyle 2\) after multiplying by \(\displaystyle 4\), so the number after \(\displaystyle 64\) is given by \(\displaystyle 64\) divided by \(\displaystyle 2\), which is \(\displaystyle 32\).

The pattern in the set is to add three every time.  The last number of the set given is 19 so add 3 and get 22.  Add 3 again and get 25. Add 3 again and get 28. Thus the answer is 

\(\displaystyle 22, 25, 28.\)

To find the next number in the sequence, we need to find the pattern. In this problem, the pattern is adding by seven! So, to find the first number, we need to subtract seven from the number after the blank.

\(\displaystyle 14 - 7 = 7\)

To find the next number in the sequence, we need to find the pattern. In this problem, the pattern is subtracting by ten! So, to find the first number, we need to subtract ten from the number before the blank.

\(\displaystyle 35 - 10 = 25\)

To find the next number in the sequence, we need to find the pattern. In this problem, the pattern is adding by threes.

\(\displaystyle 11 + 3 = 14\)