Question

Find the odd term in the sequence $1,3,8,15,24,35$
A) 0
B) 1
C) 2
D) 3
E) 4

Answer 1

Hint:
Here, we have to find the series by using the concept of logical reasoning. We will find the relation between the consecutive integers. We will find the term which does not satisfy the relation and then we will find the right term which has to be replaced instead of the wrong term so that their relation remains the same.

Complete step by step solution:
We are given a series $1,3,8,15,24,35$
We will find the relation between the consecutive terms on either side.
First, we will move the series from the left to the right.
The difference between the first term and the second term $ = 3 - 1 = 2$
The difference between the second term and the third term $ = 8 - 3 = 5$
The difference between the third term and the fourth term $ = 15 - 8 = 7$
The difference between the fourth term and the fifth term $ = 24 - 15 = 9$
The difference between the fifth term and the sixth term $ = 35 - 24 = 11$
Thus, the relation between the given consecutive integers is that their difference between the consecutive integers is the consecutive odd terms except at first two integers.
Thus, if the first term is changed to $0$, then the relation becomes the same for all the consecutive integers.
$ \Rightarrow $ If the first term is changed to $0$, then the series becomes $0,3,8,15,24,35$.
Thus, the relation between the given consecutive integers becomes that their difference between the consecutive integers is the consecutive odd terms for all integers.

Therefore, the correct series is $0, 3, 8, 15, 24, 35$ and thus Option (A) is the correct answer.

Note:
We should know that logical reasoning can be done in either the frontward direction or in the backward direction. We had done the logical reasoning in the frontward direction but if it is done in the backward direction, then the consecutive odd numbers becomes negative. It is important to find the correct term even though the relation varies in the directions. We would make a mistake in finding whether it is of the form of consecutive odd integers or in the form of consecutive prime numbers. We should avoid this error by knowing the difference between Prime numbers and Odd numbers.