Question

Find the next number of series:-
\[9,25,46,73,107{\text{ }}........\]
$\left( a \right){\text{ 133}}$
$\left( b \right){\text{ 149}}$
$\left( c \right){\text{ 148}}$
$\left( d \right){\text{ 145}}$
$\left( e \right){\text{ 151}}$

Answer 1

Hint: For solving this type of question we just need to find the relation between those numbers. Here, we can see that the difference between the two numbers is increasing with $1$ each position. So by using this concept we will be able to solve this question.

Complete step-by-step answer:
We have the series given as \[9,25,46,73,107{\text{ }}........\]
We will now find the relation between the numbers and then we will be able to put the next value.
As we can see that by finding the difference between the second and first number, we get
$ \Rightarrow 25 - 9 = 16$
Similarly, for the next pair, we will have which will be the difference between the third and second, so we get
$ \Rightarrow 46 - 25 = 21$
For the fourth and the third number, we have
$ \Rightarrow 73 - 46 = 27$
For the fifth and the fourth number we have,
$ \Rightarrow 107 - 73 = 34$
Now on comparing and analyzing the result of the differences we can see that the differences between the forth and the back number are getting increased by $1$ and mathematically we can write it as
$ \Rightarrow 21 - 16 = 5$
For the next one, it will be
$ \Rightarrow 27 - 21 = 6$
Similarly,
$34 - 27 = 7$
So for the next number, we will have the difference of $8$ , so it will be
$ \Rightarrow 42 - 34 = 8$
Hence, on adding the $42$ to the last given number in the series we get
$ \Rightarrow 107 + 42 = 149$
Therefore, on solving the series \[9,25,46,73,107{\text{ }}........\] we get the next number as $149$ .
Hence, the option $\left( b \right)$ is correct.
Note: This type of question is tricky and to solve a problem like this we need practice so that we can have all types of relations and also we should have to be updated about the question pattern. Some types of questions can be easily solved if we have the formulas at our fingertips then we can easily solve such problems.