Question

The triangular numbers are defined by the recursive formula t1 = 1, tn = tn - 1 + n, where n ∈N and n > 1. What are the first 9 triangular numbers? A) 1, 2, 4, 7, 11, 16, 22, 29, 37 B) 1, 2, 5, 9, 14, 20, 27, 35, 44 C) 1, 3, 6, 10, 15, 21, 28, 36, 45 D) 1, 3, 7, 11, 16, 22, 29, 37, 46

Answer 1

C) 1, 3, 6, 10, 15, 21, 28, 36, 45

Step-by-step explanation

The recursive formula is,

`t_1=1,t_n=t_(n-1)+n`

when n is a natural number greater than 1.

When n=2,

`t_2=t_(2-1)+2`

`t_2=t_(1)+2 = 1 + 2 = 3`

when n=3,

`t_3=t_(2)+2 = 3 + 3= 6`

when t=4,

`t_4=t_(3)+2 = 6+ 4= 10`

When t=5,

`t_5=t_(4)+5 = 10 + 5 = 15`

when t=6,.

`t_6=t_(5)+6 = 15 + 6 = 21`

when t=7

`t_7=t_(6)+7 = 21 + 7 = 28`

When t=8,

`t_8=t_(7)+8 = 28 + 8 = 36`

When t=9,

`t_9=t_(8)+9 = 36 + 9 = 45`

Hence the first nine triangular number are

C) 1, 3, 6, 10, 15, 21, 28, 36, 45