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