Question

Find: $12,15,21,24,30,33,?,?$

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 six 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 six terms. We will check which rule is applied by picking the first two terms,
If we add the first term $12$plus $3$we get $12 + 3 = 15$and after finding the second term, multiply by $2$ and $3$after that adding we get $15 + (3 \times 2) = 21$
Similarly take the third term and add it by three we get $21 + 3 = 24$again after finding the third term
$24 + (3 \times 2) = 30$since the fifth term is known thus, we will approach to the sixth term
Adding three by $30 + 3 = 33$and then as similar as before $33 + (3 \times 2) = 39$
And finally add the seventh term by three we get $39 + 3 = 42$which the required answer
Hence the sequence gone up to $12,15,21,24,30,33,39,42$(by finding the difference for addition is three also three into two for multiplication)

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.
Example: find missing numbers, $2,3,5,7,?$since the know numbers are all prime number hence the answer is $11$ which is $2,3,5,7,11$