Hint: In this question, first of all, observe the math that has been applied to get further terms in the series. Then calculate the terms by our obtained logic and find out which term is different from the terms in the given series and the terms in our obtained series. So, use this concept to reach the solution to the given problem.
Complete step-by-step solution:
Given series is \[9,19,37,75,149,297\]
Clearly, from the given series we can observe that after the next term is obtained by multiplying its preceding term with 2 and adding 1. And the further term is obtained by multiplying its preceding term by 2 and subtracting 1.
The first term in the series = 9
We can obtain the second term by multiplying the first term with 2 and adding 1.
So, second term in the series \[ = 9 \times 2 + 1 = 19\]
We can obtain the third term by multiplying the second term with 2 and subtracting 1.
So, third term in the series \[ = 19 \times 2 - 1 = 38 - 1 = 37\]
We can obtain the fourth term by multiplying the third term with 2 and adding 1.
So, fourth term in the series \[ = 37 \times 2 + 1 = 74 + 1 = 75\]
We can obtain the fifth term by multiplying the fourth term with 2 and subtracting 1.
So, fifth term in the series \[ = 75 \times 2 - 1 = 150 - 1 = 149\]
We can obtain the sixth term by multiplying the fifth term with 2 and adding 1.
So, sixth term in the series \[ = 149 \times 2 + 1 = 298 + 1 = 299\]
But, in the series, it is given that the sixth term is 297.
So, the wrong number in the series is 297.
Thus, the correct option is E. 297
Note: To solve these types of problems, the series is given by doing simple math applications like addition, subtraction, multiplication, and division. These math applications may be done one at a time or two at a time to form the series. So, identify them and then solve them accordingly.