Its $36 if it is only for his three roommates
and
$27 if it is only for his three roommates w/ Jason
Answer:
![\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Ctext%7Bsixth%20term%20is%20equal%20to%7D%5C%20%5Cdfrac%7B1%7D%7B1024%7D%7D)
Step-by-step explanation:
The explicit formula for a geometric sequence:
![a_n=a_1r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1r%5E%7Bn-1%7D)
- n-th term
- first term
- common ratio
![r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Ba_2%7D%7Ba_1%7D%3D%5Cdfrac%7Ba_3%7D%7Ba_2%7D%3D...%3D%5Cdfrac%7Ba_n%7D%7Ba_%7Bn-1%7D%7D)
We have
![a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...](https://tex.z-dn.net/?f=a_1%3D-1%2C%5C%20a_2%3D%5Cdfrac%7B1%7D%7B4%7D%2C%5C%20a_3%3D-%5Cdfrac%7B1%7D%7B6%7D%2C%5C%20...)
The common ratio:
![r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B%5Cfrac%7B1%7D%7B4%7D%7D%7B-1%7D%3D-%5Cdfrac%7B1%7D%7B4%7D%5C%5C%5C%5Cr%3D%5Cdfrac%7B-%5Cfrac%7B1%7D%7B6%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D-%5Cdfrac%7B1%7D%7B6%7D%5Ccdot%5Cdfrac%7B4%7D%7B1%7D%3D-%5Cdfrac%7B2%7D%7B3%7D%5Cneq-%5Cdfrac%7B1%7D%7B4%7D)
<h2>It's not a geometric sequence.</h2>
If
then the common ratio is ![r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B-%5Cfrac%7B1%7D%7B16%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D-%5Cdfrac%7B1%7D%7B16%7D%5Ccdot%5Cdfrac%7B4%7D%7B1%7D%3D-%5Cdfrac%7B1%7D%7B4%7D)
Put to the explicit formula:
![a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D-1%5Cleft%28-%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5E%7Bn-1%7D)
Put
and solve for <em>n </em>:
![-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1](https://tex.z-dn.net/?f=-1%5Cleft%28-%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5E%7Bn-1%7D%3D%5Cdfrac%7B1%7D%7B1024%7D%5Cqquad%5Ctext%7Buse%7D%5C%20a%5En%3Aa%5Em%3Da%5E%7Bn-m%7D%5C%5C%5C%5C-%5Cleft%28-%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5En%3A%5Cleft%28-%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5E1%3D%5Cdfrac%7B1%7D%7B1024%7D%5C%5C%5C%5C-%5Cleft%28-%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5En%5Ccdot%28-4%29%3D%5Cdfrac%7B1%7D%7B1024%7D%5C%5C%5C%5C%284%29%5Cleft%28-%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5En%3D%5Cdfrac%7B1%7D%7B1024%7D%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%204%7D%5C%20%5Ctext%7B%2Fmultiply%20both%20sides%20by%7D%5C%20%5Cdfrac%7B1%7D%7B4%7D%2F%5C%5C%5C%5C%5Cleft%28-%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5En%3D%5Cdfrac%7B1%7D%7B4096%7D%5C%5C%5C%5C%5Cdfrac%7B%28-1%29%5En%7D%7B4%5En%7D%3D%5Cdfrac%7B1%7D%7B4%5E6%7D%5Cqquad%20n%5C%20%5Ctext%7Bmust%20be%20even%20number.%20Therefore%7D%5C%20%28-1%29%5En%3D1)
![\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%5En%7D%3D%5Cdfrac%7B1%7D%7B4%5E6%7D%5Ciff%20n%3D6)
Answer:
x1, x2 = 4.74 , -2.74
Step-by-step explanation:
To find the roots of a quadratic function we have to use the bhaskara formula
ax^2 + bx + c
x^2 - 2x - 13
a = 1 b = -2 c = -13
x1 = (-b + √ b^2 - 4ac)/2a
x2 =(-b - √ b^2 - 4ac)/2a
x1 = (2 + √ (2^2 - 4 * 1 * (-13)))/2 * 1
x1 = (2 + √ (4 + 52)) / 2
x1 = (2 + √ 56 ) / 2
x1 = (2 + 7.48) / 2
x1 = 9.48 / 2
x1 = 4.74
x2 = (2 - √ (2^2 - 4 * 1 * (-13)))/2 * 1
x2 = (2 - √ (4 + 52)) / 2
x2 = (2 - √ 56 ) / 2
x2 = (2 - 7.48) / 2
x2 = -5.48 / 2
x2 = -2.74
Answer:
254.47 m or B
Step-by-step explanation:
First you find the area of the circle and then you subtract it from the area of the square to get your answer.
Hope it helps c:
Answer:
6 neighbors
Step-by-step explanation:
1 bread can be given to 2 neighbors when cut in half(1/2). This case, you have 3 bread so 3x2=6