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 10th row of this arrangement:

• A. 1000

Answer 1

The correct option is A 1000
Sum of elements of the first row = 1
Sum of elements of the second row = 3+5 = 8
Sum of elements of the third row = 7+9+11 = 27
If you observe, the pattern looks like 1, 8, 27 i.e., $1^3,2^3,3^3,....$.
To verify it, calculate the sum of elements of the fourth row.
Sum of elements of the fourth row = 13+15+17+19 = 64 = $4^3$
So, sum of elements of the tenth row = ${10}^3=1000$