In this set, each subsequent fraction is half the size of the preceding fraction; (the denominator is doubled for each successive fraction, but the numerator stays the same). Given that the last fraction in the set is , it follows that the subsequent fraction will be . 

A prime number only has two factors, one and itself.   and  are the only values given that have that property.  But the range of the set is between  and  which means that the answer cannot be  since it is greater than .  That means the final answer is .

The equation for the average would be 

.

To work backwards you must first multiple both sides by .  

This gives us .  

To solve for , you must subtract all the other values from .  

This gives us an answer of .

The numbered cards in a deck range from  to .  

Since  is not in the above set, it is the missing NUMBER card from the deck.

King and Ace are incorrect choices as they are called face cards in a deck of cards.

Add 5 to the first element to get the second element. The increment increases by two with each successive entry. The pattern can be seen below:

 - this is the correct response

This is confirmed by noting:

There are three things going on with these patterns.

First, the number of dots in the pattern is increasing by one, so there must be four dots in the correct choice. However, this does not eliminate any of the choices.

Second, the sector that included the dots alternates between lower right and upper left, so the correct choice must have its dots in the upper left sector. This eliminates figures (c) and (d) and leaves (a) and (b) as possible choices.

Third, the shaded sector is rotating clockwise. The shaded sector in the correct choice must be the one at the lower left, thereby eliminating (b) and leaving (a) as the correct choice.

Taking only shapes into account, the sequence is:

Triangle, circle, square,

Triangle, circle, square,

Triangle, ?

To continue the cycle, the next shape must be a circle.

Now, taking only coloration into account, the sequence is:

Left half shaded, unshaded,

Top half shaded, unshaded,

Left half shaded, unshaded,

Top half shaded, ?

To continue the cycle, the next shape must be unshaded.

Therefore, the correct choice is the unshaded circle, Figure (c).

Taking only shapes into account, the sequence is:

Triangle(s), square(s). circle(s),

Triangle(s), square(s). circle(s),

Triangle(s)...

To continue the pattern, the next figure must comprise one or two squares.

Taking only number and color of shapes into account, the sequence is

One white, one black over one white, one black, one white over one black,

One white, One black over one white, one black,...

To continue the pattern, the next figure must comprise one white shape over one black. 

Therefore, the correct choice is one white square over one black square, which is Figure (b).

The way to get from one entry of the sequence to the next alternates between multiplying by two and adding one, as follows:

Continuing the pattern:

, the correct choice.