Question

Find the series of this number \[3{\text{,}}11{\text{,}}25{\text{,}}45{\text{,?}}\]

Answer 1

Hint: In this question we are going to find the missing number in the given series. To find the missing term primarily we need to find the pattern existing between the given numbers. The pattern follows a logical rule based on elementary arithmetic. After identifying the pattern we can compute the missing term easily.

Complete step by step solution:
Let's consider the missing term be \[x\].
In order to determine the series of this number \[3{\text{,}}11{\text{,}}25{\text{,}}45{\text{,?}}\]
That is, the first term in the series is \[3\], second term is \[11\], third term is \[25\], fourth term is \[45\] and the fifth term is missing let it be \[x\].
To find the pattern in the series, first find the differences between each term and its succeeding term.
The difference between the first and second term is, \[11 - 3 = 8\].
 The difference between the second and third term is, \[25 - 11 = 14\].
The difference between the third and fourth term is, \[45 - 25 = 20\].
We can see that the difference between the results is \[6\], that is, each term increases by \[6\] with the difference of the preceding term.
To find the missing term: add the preceding term, the difference of the preceding terms and \[6\].
Here the missing term is \[x\], the preceding term of \[x\] is \[45\], the difference of the preceding terms \[45\] and \[25\] is \[20\].
\[\therefore x = 45 + 20 + 6\]
By adding it, we will get \[x = 71\].
Therefore, the missing term is \[71\] and the series is \[3{\text{,}}11{\text{,}}25{\text{,}}45{\text{,71}}\].
So, the correct answer is “71”.

Note: The given question is based on mathematical reasoning. To solve these types of questions one should properly understand the question and list out what is given and what needs to be found. Then try to find the relation between the terms in the series. The relationship between each term is any kind of mathematical relation. So one should closely analyse the terms to find the relation.