Question

Find the missing number 389,338,297,……………245.
A.266
B.276
C.256
D.286
E.255

Answer 1

Hint: Here, we will find the fourth term by using the concept of number analogy. We will find the relation between the consecutive terms either by any one of the arithmetic operations like addition, subtraction, multiplication or division. Then using the same relation we will find the missing number.

Complete step-by-step answer:
We are given a series of numbers 389,338,297,……………245.
Now, we will find the relation between the consecutive integers to find the missing number.
Now, considering the first two numbers, we get
The difference between the first two integers 389 and 338 is 51.
Now, considering the second number and the third number, we get
The difference between the second number and the third number 389 and 297 is 41.
Now, we will find the relation between these differences of the first two consecutive integers and the next two consecutive integers.
So, we get the difference between the differences of the first two consecutive integers and the next two consecutive integers
 $51 - 41 = 10$
So, the difference between the second number and the third number and the third number and the fourth number would be 31 so that the difference between the differences between the second number and the third number and the third number and the fourth term is 10.
So, we get the fourth term by subtracting 31 from the third term.
$297 - 31 = 266$
So, the fourth term is 266.
Therefore, the fourth term in the series of numbers 389,338,297,……………245 is 266.
Thus option (A) is the correct answer.

Note: We should note that we can verify the relation between the missing term and the next term has the same relation between the consecutive terms as before. We have to find the fourth term as 266 and the next term as 245. The difference between the fourth term and the fifth term is $21$. Thus the difference between the differences of the third number and the fourth number and the fourth term and the fifth term will be 10. So, the relation between the given series of numbers is that their differences between the consecutive terms is decreasing by 10.