In the following sequence of triangular numbers, how many dots will be present in the 5th (next) triangle?

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Solution

The correct option is D 15
The number of dots in a triangle representing a triangular number sequence follows the rule $[n \times (n + 1)] \div 2$ .
Hence, for the 5th triangle, n = 5.

$∴$ Number of dots in the 5th triangle
= $[5 \times (5 + 1)] \div 2$ = $[5 \times 6] \div 2$
= $30 \div 2$ = 15

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