Mathematics: Write the sum using summation notation, assuming the suggested pattern continues. 6, -18, 54, -162, +… Is this sequence arithmetic or geometric? Explain your answer.

Write the sum using summation notation, assuming

Ответ:

soliseric879

31.08.2021

Mathematics

Hello,

This sequence is geometric with a ratio of -3

the first term is 6

Step-by-step explanation:

$u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\$

serie does not converge.

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Ответ:

meganenaranjo

24.05.2020

Mathematics

TV = 3x+9 - (14+2x)

TV = 3x + 9 -14 - 2x

TV = x - 5

U = ((3x + 9) + (14 + 2x)) / 2

U = (5x + 23) / 2

TU = (2(3x + 9) / 2) - (5x+23)/2

TU = (6x + 18 - 5x -23) /2

TU = (x - 5) / 2

Since U is the midpt, UV = TU, so UV = (x-5) / 2

TU + UV = TV

(x-5) / 2 + (x-5) /2 = 2 (x-5) /2 = x-5 = TV

Use a number for x. Let's use 10.

T is 39, V = 34

U = (39 + 34)/2 = 73/2 = 36.5

TV = 39-34 = 5

TV from our equation is x-5. 10 - 5 = 5.

TU and UV = (x-5) / 2. (10-5) /2 = 5/2.

(39-34)/2 = 5/2

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Write the sum using summation notation, assuming the suggested pattern continues. 6, -18, 54, -162, +… Is this sequence arithmetic or geometric? Explain your answer.

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