Expand the left and the right side .
![3x + 2x + 8 = x - x - 2](https://tex.z-dn.net/?f=3x%20%2B%202x%20%2B%208%20%3D%20x%20-%20x%20-%202)
then you simplify
![5x + 8 = - 2](https://tex.z-dn.net/?f=5x%20%2B%208%20%3D%20%20-%202)
then continue ...
you will get x = -2
Answer:
A formula for the nth term of the given sequence is:
![a_n=36\left(-\frac{4}{3}\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D36%5Cleft%28-%5Cfrac%7B4%7D%7B3%7D%5Cright%29%5E%7Bn-1%7D)
Step-by-step explanation:
Given the sequence
36, -48, 64...
We know that a geometric sequence has a constant ratio r and is defined by
![a_n=a_1\cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1%5Ccdot%20r%5E%7Bn-1%7D)
Compute the ratios of all the adjacent terms
![\frac{-48}{36}=-\frac{4}{3},\:\quad \frac{64}{-48}=-\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-48%7D%7B36%7D%3D-%5Cfrac%7B4%7D%7B3%7D%2C%5C%3A%5Cquad%20%5Cfrac%7B64%7D%7B-48%7D%3D-%5Cfrac%7B4%7D%7B3%7D)
The ratio of all the adjacent terms is the same and equal to
![r=-\frac{4}{3}](https://tex.z-dn.net/?f=r%3D-%5Cfrac%7B4%7D%7B3%7D)
Therefore, the given sequence is a geometric sequence.
As the first element of the sequence is
![a_1=36](https://tex.z-dn.net/?f=a_1%3D36)
so substituting
and
in the nth term
![a_n=a_1\cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1%5Ccdot%20r%5E%7Bn-1%7D)
![a_n=36\left(-\frac{4}{3}\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D36%5Cleft%28-%5Cfrac%7B4%7D%7B3%7D%5Cright%29%5E%7Bn-1%7D)
Therefore, a formula for the nth term of the given sequence is:
![a_n=36\left(-\frac{4}{3}\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D36%5Cleft%28-%5Cfrac%7B4%7D%7B3%7D%5Cright%29%5E%7Bn-1%7D)
<span>twelve million, three hundred twenty-four thousand, nine hundred four</span>
we know that
The sum of all interior angles in the polygon is equal to the formula
![(n-2)*180\°](https://tex.z-dn.net/?f=%28n-2%29%2A180%5C%C2%B0)
where
n is the number of sides of the polygon
In this problem we have
![n=6](https://tex.z-dn.net/?f=n%3D6)
substitute the value in the formula
![(6-2)*180\°=720\°](https://tex.z-dn.net/?f=%286-2%29%2A180%5C%C2%B0%3D720%5C%C2%B0)
<u>Find the value of x</u>
![720\°=x\°+108\°+113\°+132\°+75\°+160\°\\720\°=x\°+588\°\\x\°=720\°-588\°\\x=132\°](https://tex.z-dn.net/?f=720%5C%C2%B0%3Dx%5C%C2%B0%2B108%5C%C2%B0%2B113%5C%C2%B0%2B132%5C%C2%B0%2B75%5C%C2%B0%2B160%5C%C2%B0%5C%5C720%5C%C2%B0%3Dx%5C%C2%B0%2B588%5C%C2%B0%5C%5Cx%5C%C2%B0%3D720%5C%C2%B0-588%5C%C2%B0%5C%5Cx%3D132%5C%C2%B0)
therefore
<u>the answer is</u>
the measure of x is ![132\°](https://tex.z-dn.net/?f=132%5C%C2%B0)