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

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

EXPLANATION

The recursive formula is,

when n is a natural number greater than 1.

When n=2,

when n=3,

when t=4,

When t=5,

when t=6,.

when t=7

When t=8,

When t=9,

Hence the first nine triangular number are

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

the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. hope this ! mark brainliest! you v much! : )

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1