Question

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

Answer 1

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.