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 \(\displaystyle 26 + 9 = 35\).