Answer:
The formula which can be used to describe the sequence is:
⇒ 3rd answer
Step-by-step explanation:
The terms of the sequence are -81, 108, -144, 192, ...
∵ 108 ÷ -81 = ![-\frac{4}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B3%7D)
∵ -144 ÷ 108 = ![-\frac{4}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B3%7D)
∵ 192 ÷ -144 = ![-\frac{4}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B3%7D)
- There is a constant ratio between each two consecutive terms
∴ The sequence is a geometric sequence
The formula of the nth term of the geometric sequence is
, where a is the first term and r is the constant ratio between each two consecutive terms
∵ The first term is -81
∴ a = -81
∵ The constant ratio =
∴ r = ![-\frac{4}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B3%7D)
- Substitute then in the formula above
∴ ![a_{n}=-81(\frac{-4}{3})^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3D-81%28%5Cfrac%7B-4%7D%7B3%7D%29%5E%7Bn-1%7D)
Assume that
= f(x)
∴ n = x
∴ ![f(x)=-81(\frac{-4}{3})^{x-1}](https://tex.z-dn.net/?f=f%28x%29%3D-81%28%5Cfrac%7B-4%7D%7B3%7D%29%5E%7Bx-1%7D)
The formula which can be used to describe the sequence is:
![f(x)=-81(\frac{-4}{3})^{x-1}](https://tex.z-dn.net/?f=f%28x%29%3D-81%28%5Cfrac%7B-4%7D%7B3%7D%29%5E%7Bx-1%7D)
1- (-2) = 3
4- (-1)= 5
3/5 is the slope to find the distance
Answer:
5 units
Step-by-step explanation:
If point T is on the line segment SU, then ST + TU = SU.
Given
TU = 4x + 1
SU = 8
ST = 3x
To get TU, we need to get the value of x first. To get x, we will substitute the given parameters into the formula;
3x+4x+1 = 8
7x+1 = 8
subtract 1 from both sides
7x+1-1 = 8-1
7x = 7
divide both sides by 7
7x/7 = 7/7
x = 1
Substitute x = 1 into the length TU
Since TU = 4x+1
TU = 4(1)+1
TU = 5
Hence the numerical length of TU is 5 units
Independence Day, commonly known as the Fourth of July, is a federal holiday in the United States commemorating the adoption of the Declaration of Independence on July 4, 1776, declaring independence from the Kingdom of Great Britain.
True
11 is √121
12 is √144
So √131 is in between 11 and 12