The ( n^{th} ) triangular number is given by [ T_n = \dfrac{n(n+1)}{2} ]
15th triangular number: [ T_{15} = \dfrac{15 \times 16}{2} = 120 ]
Triangle of dots for ( n = 5 ):
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(5 rows with 1, 2, 3, 4, 5 dots respectively; total ( T_5 = 15 ) dots.)
Answer: 15th triangular number = 120