Fill in the blank: \[62,66,63,66,64,\_\_,65,............\]
A. 60
B. 61
C. 62
D. 66

Hint: In this question, first of all find the difference between consecutive terms in the series which will give us an idea about the series. Then assume which number suits the missing blank and prove that our assumption is correct by applying it to the further term. So, use this concept to reach the solution of the given problem.

Complete step by step answer:
Given series is \[62,66,63,66,64,\_\_,65,............\]
Follow the given below steps to achieve the answer:
Step 1: First find the difference between the first two numbers.
             \[66 - 62 = 4\]
              So, here ‘4’ is added to the first term to get the second term in the series.
Step 2: Then find the difference between the next two consecutive terms in the series.
              \[63 - 66 = - 3\]
               So, here ‘3’ is subtracted from the second term to have the third term in the series.
Step 3: Next find the difference between third and fourth term in the series.
              \[66 - 63 = 3\]
              So, here ‘3’ is added to the third term to get the fourth term in the series.
Step 4: Then find the difference between fourth and fifth term in the series.
             \[64 - 66 = - 2\]
              So, here ‘2’ is subtracted from the fourth term to get the fifth term in the series.
In the given series we can see that 4 is added and 3 is subtracted to get next terms. Then 3 is added and 2 is subtracted to get the next terms. Further 2 is to be added and 1 is to be subtracted to get the next terms in the given series.
Step 5: So, to get our required answer we have to add ‘2’ to the fifth term in the series.
              \[64 + 2 = 66\]
Therefore, the missing term is 66. To prove our assumption is right, we will proceed to the further step in where we have to subtract ‘1’ from the missing term to get the seventh term in the series.
Step 6: Here, we have to subtract ‘1’ from the missing term to have the next term in the series.
              \[66 - 1 = 65\]
Since, this obtained term matches to the given seventh term in the series our assumption is proved.
Thus, the correct option is D. 66

Note: The next terms in the series can be obtained by adding 1 and subtracting 0. Then adding 0 and subtracting – 1 and so on. So, consecutive integers should be added and subtracted to complete the given series.