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Question

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

A
A
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B
B
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C
C
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D
D
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Solution

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
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
21, 28 and 36 are triangular numbers.

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