First, determine what the pattern is in the series. The pattern here is to multiply the previous number by 2 and then add 1. Therefore, multiply 47 by 2 (which is 94), and then add 1. The result is 95.

In this sequence, every subsequent number is 7 less than the preceding number. Given that the number that precedes w is 71, the value of w is $\displaystyle 71-7=64$. Therefore, 64 is the correct answer. 

The numbers increase by 5. Given that the number before n is 20, the value of n is $\displaystyle 20+5=25$.

What is the next term in the following sequence?

$\displaystyle \left \{ 4,11,18,25,32... \right \}$

This is an arithmetic sequence with a common difference of $\displaystyle 7$. To find the next term in an arithmetic sequence, add the common difference to the previously listed term:

$\displaystyle 32+7=39$

In this sequence, the difference between each number is double the difference between the number that came prior to it in the sequence. For example, $\displaystyle 8-5=3$ and $\displaystyle 14-8=6$. Thus, the missing number must be greater than $\displaystyle 14$ by a difference of $\displaystyle 12$ and therefore $\displaystyle 14 + 12= 26$

In this sequence of numbers, there is an important pattern to recognize. In this sequence each number is a prime number, however the sequence skips every other prime number. Thus, the sequence begins with the prime number $\displaystyle 1$ and then skips the prime number $\displaystyle 2$ (which is the only even prime number) and goes to $\displaystyle 3$. From $\displaystyle 3$ the next prime number is $\displaystyle 5$, however since the pattern in this sequence skips every other prime number--the missing number is $\displaystyle 7$.      

In this sequence of numbers, there is an important pattern to recognize. Each number in this sequence is a composite number--however, the sequence skips every other composite number. Thus, the next composite number after $\displaystyle 8$ is $\displaystyle 9$--which is skipped because of the pattern, making the correct answer $\displaystyle 10$.

In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of $\displaystyle 7$. In other words, each number in this list is a multiple of $\displaystyle 7$. Thus, $\displaystyle 35 + 7= 42$ 

In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of $\displaystyle 4$. Thus, the correct answer is $\displaystyle 25$, because $\displaystyle 21 + 4=25$  

In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of 9. Thus, the correct answer is $\displaystyle 35$ because $\displaystyle 26 + 9 = 35$.