Question

Find the missing number $8,15,28,53,?,199$

Answer 1

First we have to define what the terms we need to solve the problem are.
Select two or three terms to the text which rule will be applied to find the missing number.
For example; if you have $5$ numbers in a series then pick the first two or three numbers and compare.

Complete step by step answer:
Since the known values are four in the given question, while choosing the number to check the rule, select the number that is easy to operate.
Thus, the given sequence has four terms. We will check which rule is applied by picking the first two terms,
The first term is $8$ and if we add the first term by $2$ we will get $8 \times 2 = 16$ and then subtract solution which we found by one then we get $(8 \times 2) - 1 = 16 - 1 = 15$ which is the second term given in the sequence thus for the first term $(n \times 2) - 1$ is applied.
Again, take the second term $15$ and multiple by two we get $15 \times 2 = 30$ but here subtracts the solution by two so that only we can able to get the third term that it $(15 \times 2) - 2 = 30 - 2 = 28$
Similarly, to find the fourth term by same method $(28 \times 2) - 3 = 56 - 3 = 53$ here we subtracted by three
For all terms to find the next term we need to multiple by two and subtract by n-1 term like one, two, three,
Hence to find the fifth term we apply $(53 \times 2) - 4$ (it is fifth term so we apply n-1 which is 4)
Therefore $(53 \times 2) - 4 = 106 - 4 = 102$ is the required answer.
Also check the last sixth term which is $199 = (102 \times 2) - 5$ (sixth term we need to subtract by five)
Hence the missing term is $102$.

Note: first identify the order of the number given is ascending or descending number and calculate the differences between those that are next to each other and finally estimate the difference between numbers to calculate the missing number.