Question

Find the 14th and 15th triangular numbers and find their sum verify the statement 8 for this sum.

Answer 1

14th triangular number = 1 + 2 + 3+4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 = 105.

15th triangular number = 1 + 2 + 3 + 4 + ___ + 15 = 120

Sum of 105 + 120 = 225

According to statement 8, the sum of 14th and 15th triangular numbers in equal to

n + (n + 1) = (n + 1)2

105 + 120 = (14+ 1)2

225 = 225.