Question

The odd positive integers are arranged in a triangle as follows:
1
3 5
7 9 11
13 15 17 19
21 23 25 27 29
... ... ... ... ... ...
... ... ... ... ... ...
Find the sum of the numbers in the nth row of this arrangement:

• A. $n^2+n$
• B. $2n^2-2+n$
• C. $n^3$
• D. None of these

Answer 1

The correct option is C $n^3$

Let's check the options one by one.
First is $n^2+n$ which clearly gives the value 2 when n = 1, we can see that in the first row, it is 1. hence this option is not possible.
For the second option, it fails to satisfy the sum in the third row and so on.
Clearly, the third option satisfies the sum of the numbers in all the rows one by one. Hence, it is the correct answer.