Question

Find the missing term in the following series.
0, 4, 18, 48, ?, 180
(A) 100
(B) 191
(C) 152

Answer 1

Hint: Every term in the given series can be written in a general form. Just decode every term and write them in products of numbers. So in this series, the nth term can be written as n square multiplied by its previous number i.e. $\left( {n - 1} \right) \times {\left( n \right)^2}$ where n-1 will be the previous term of n. Using this, find the missing term.

Complete step-by-step answer:
We are given a series 0, 4, 18, 48, ?, 180 and we have to find the missing term.
Since it is a series every term is obtained from a general from. Let’s decode the general form.
First term is 0.
Zero can be written as $0 \times {1^2}$
Second term is 4.
4 can be written as $1 \times {2^2}$
Third term is 18.
18 can be written as $2 \times {3^2}$
Fourth term is 48.
48 can be written as $3 \times {4^2}$
Fifth term is missing.
Sixth term is 180.
180 can be written as $5 \times {6^2}$
So, as we can see every term in the series is written as the square of the number of the term multiplied by its previous numbered term.
$\left( {n - 1} \right) \times {\left( n \right)^2}$
So here the fifth term is missing.
n=5
Fifth term will be
$
 \left( {n - 1} \right) \times {\left( n \right)^2} \\
  = \left( {5 - 1} \right) \times {\left( 5 \right)^2} \\
  {\left( 5 \right)^2} = 25 \\
  = 4 \times 25 \\
  = 100 \\
 $
Therefore, the missing (fifth) term is 100.
From among the options given in the question, Option A is correct.
So, the correct answer is “Option A”.

Note: This is an arithmetic aptitude question. These questions are used to determine a skill or ability of a person. Whenever these types of questions are given, first consider each term given and decode them into a general form or whether there is a similarity between each term or not. This makes the solution easy.