Question: Which number would come in the place of the underline mark in the series \[3,9,21,\\_\\_\\_\\_ 93\] ...

Question

Which number would come in the place of the underline mark in the series $3,9,21,\\_\\_\\_\\_ 93$ ?
A. $38$
B. $45$
C. $47$
D. $51$

Answer 1

Solution

In this question, we need to find the missing number in the series $3,9,21,\\_\\_\\_\\_ 93$ . Sequence is nothing but a collection of elements in which repetitions are also allowed whereas series is the sum of all the elements in the sequence. First, we need to compare the second term of the series with the first term and then we need to observe what kind of relationship that they have. After that we can simply apply the relations to the next upcoming terms and then can proceed further.

Complete step-by-step answer:
Given, $3,9,21,\\_\\_\\_\\_ 93$
Here we need to find the next term.
Now , we can compare the second term of the series with the first term
That is, we can find the difference between the first and second term.
On subtracting first term from second term,
We get,
$9 – 3 = 6$
Now let us compare the second term of the series with the third term.
$21 – 9 = 12$
On observing the difference, all are the multiple of $6$ . Similarly, the third difference will be $18$ and then the fourth difference will $24$ . If we proceed like this , then $93$ can’t be the last term.
Thus let us consider the difference as $6,12,24\ \ldots$
Now on adding the third difference with the third number given in the series, we can find the fourth term.
On adding $24$ with $21$ ,
We get,
The fourth term is $45$ .
Thus the next term of the series $3,9,21,\\_\\_\\_\\_ 93$ is $45$ .
Final answer :
The next term of the series $3,9,21,\\_\\_\\_\\_ 93$ is $45$ .
Option B). $45$ is the correct answer.

So, the correct answer is “Option B”.

Note: In order to solve these types of questions, we should be aware of various types of basic patterns like increasing and decreasing, multiplication, division, square, etc. being used in a series formation. A series is nothing but a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. We should also be careful finding the difference between the terms of the series.