Question

Which number should replace the question mark \[8,15,24,35,?\]
A. \[42\]
B. \[52\]
C. \[48\]
D. None of these

Answer 1

Hint: In this question, we need to find the number missing in the given series \[8,15,24,35,?\] .First, we need to check whether the given series is showing an increasing or decreasing pattern. Then we need to check whether the difference between the two consecutive terms of a series is the same or is changing, that is whether the difference is increasing or decreasing. Then we have to check whether the series is changing slowly or rapidly . From this we can understand the pattern of the series.

Complete step-by-step answer:
Given \[8,15,24,35,?\]
First, we can rewrite each term of the series in the form ,
\[8 = 3^{2} – 1\]
Then \[15\] as \[4^{2} – 1\]
Next \[24\] as \[5^{2} – 1\]
Finally, \[35\] as \[6^{2} – 1\]
Here, it is observed that the required series is of the form \[\left( n^{2} \right) – 1\] where \[n\] starts from \[3,4,5,\ldots\]
Hence the next term is \[7^{2} – 1\]
On simplifying,
We get,
\[\Rightarrow \ 48\]
Thus the next term is \[48\] .
Hence the series is \[8,15,24,35,48\]
Final answer-
The missing term is \[48\] .
Hence the series is \[8,15,24,35,48\]
Option C) . \[48\] is the correct answer.

So, the correct answer is “Option C”.

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.