Question

Which of the following triangles represent a collection of triangular numbers?

• A. A
• B. B
• C. C
• D. D

Answer 1

Answer: (C), (D)

The correct options are
C C
D D

Triangular numbers are derived from the addition of consecutive natural numbers.
1
1+2=3
1+2+3=6
1+2+3+4=10 and so on.
In triangle C,
15 = 1+ 2 + 3 + 4 + 5
21 = 1+ 2 + 3 + 4 + 5 + 6
28 = 1+ 2 + 3 + 4 + 5 + 6 +7
$\therefore$ 15, 21and 28 are triangular numbers.

In triangle D,
21 = 1+ 2 + 3 + 4 + 5 + 6
28 = 1+ 2 + 3 + 4 + 5 + 6 + 7
36 = 1+ 2 + 3 + 4 + 5 + 6 +7 +8
$\therefore$ 21, 28 and 36 are triangular numbers.