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tekilochka [14]
3 years ago
5

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
Mathematics
1 answer:
GalinKa [24]3 years ago
3 0

ANSWER

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

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

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Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

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