The 12th term of the given geometric sequence is equal to -8,388,608.
<u>Given the following sequence:</u>
<h3>What is a geometric sequence?</h3>
A geometric sequence can be defined as a series of real and natural numbers that are generally calculated by multiplying the next number by the same number each time.
Mathematically, a geometric sequence is given by the expression:
![a_n =a_1r^{n-1}](https://tex.z-dn.net/?f=a_n%20%3Da_1r%5E%7Bn-1%7D)
<u>Where:</u>
- a is the first term of a geometric sequence.
Substituting the given parameters into the formula, we have;
![a_{12} =2 \times -4^{12-1}\\\\a_{12} =2 \times -4^{11}\\\\a_{12} =2 \times -4194304](https://tex.z-dn.net/?f=a_%7B12%7D%20%3D2%20%5Ctimes%20-4%5E%7B12-1%7D%5C%5C%5C%5Ca_%7B12%7D%20%3D2%20%5Ctimes%20-4%5E%7B11%7D%5C%5C%5C%5Ca_%7B12%7D%20%3D2%20%5Ctimes%20-4194304)
12th term = -8,388,608.
Read more on geometric sequence here: brainly.com/question/12630565
M=slope
In this case the slope would be $25
y=mx+b
y=25x+45
Answer: m=25
Answer:
The price is $1.6 per square foot of the land
Step-by-step explanation:
step 1
Find the area of the plot of land
we know that
The area of the plot of land is equal to the area of trapezoid 1 plus the area of trapezoid 2
see the attached figure to better understand the problem
Remember that
The area of a trapezoid is equal to
![A=\frac{1}{2}[b1+b2]h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Bb1%2Bb2%5Dh)
<em>Find the area of trapezoid 1</em>
we have
![b1=125\ ft](https://tex.z-dn.net/?f=b1%3D125%5C%20ft)
![b2=265\ ft](https://tex.z-dn.net/?f=b2%3D265%5C%20ft)
![h=260-150=110\ ft](https://tex.z-dn.net/?f=h%3D260-150%3D110%5C%20ft)
substitute
![A1=\frac{1}{2}[125+265](110)](https://tex.z-dn.net/?f=A1%3D%5Cfrac%7B1%7D%7B2%7D%5B125%2B265%5D%28110%29)
![A1=21,450\ ft^{2}](https://tex.z-dn.net/?f=A1%3D21%2C450%5C%20ft%5E%7B2%7D)
<em>Find the area of trapezoid 2</em>
we have
![b1=150\ ft](https://tex.z-dn.net/?f=b1%3D150%5C%20ft)
![b2=265\ ft](https://tex.z-dn.net/?f=b2%3D265%5C%20ft)
![h=150\ ft](https://tex.z-dn.net/?f=h%3D150%5C%20ft)
substitute
![A2=\frac{1}{2}[150+265](150)](https://tex.z-dn.net/?f=A2%3D%5Cfrac%7B1%7D%7B2%7D%5B150%2B265%5D%28150%29)
![A2=31,125\ ft^{2}](https://tex.z-dn.net/?f=A2%3D31%2C125%5C%20ft%5E%7B2%7D)
The area total of the land is
![A=A1+A2](https://tex.z-dn.net/?f=A%3DA1%2BA2)
![A=21,450+31,125=52,575\ ft^{2}](https://tex.z-dn.net/?f=A%3D21%2C450%2B31%2C125%3D52%2C575%5C%20ft%5E%7B2%7D)
step 2
Find the price per square foot of the land
Divide the total cost by the total area
![\frac{84,120}{52,575}=1.6\frac{\$}{ft^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B84%2C120%7D%7B52%2C575%7D%3D1.6%5Cfrac%7B%5C%24%7D%7Bft%5E%7B2%7D%7D)
The original price is $70