The quotient of 4.2 and a number is less than or equal to 21.
Answer: 36 yards
Step-by-step explanation:
26 ÷ 2 = 13
13 yards = 3 tries
13 × 3 = 36 yd
3 × 3= 9
Answer:
![c(n)=4\cdot(-\frac{1}{3})^{n-1}](https://tex.z-dn.net/?f=c%28n%29%3D4%5Ccdot%28-%5Cfrac%7B1%7D%7B3%7D%29%5E%7Bn-1%7D)
Explanation:
In the given geometric sequence:
![4,-\frac{4}{3},\frac{4}{9},-\frac{4}{27},\frac{4}{81},\ldots](https://tex.z-dn.net/?f=4%2C-%5Cfrac%7B4%7D%7B3%7D%2C%5Cfrac%7B4%7D%7B9%7D%2C-%5Cfrac%7B4%7D%7B27%7D%2C%5Cfrac%7B4%7D%7B81%7D%2C%5Cldots)
We see that:
• The first term, c1 = 4
Also:
![-\frac{4}{3}\div4=-\frac{4}{3}\times\frac{1}{4}=-\frac{1}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B3%7D%5Cdiv4%3D-%5Cfrac%7B4%7D%7B3%7D%5Ctimes%5Cfrac%7B1%7D%7B4%7D%3D-%5Cfrac%7B1%7D%7B3%7D)
• The common ratio, r= -1/3
The explicit formula for a geometric function is obtained using the formula:
![f(n)=a\cdot r^{n-1}](https://tex.z-dn.net/?f=f%28n%29%3Da%5Ccdot%20r%5E%7Bn-1%7D)
Substituting a (the first term, c(1)) and r, we have the explicit formula below:
<span>90.0550458716 is the answer</span>
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![- 1 + 14x = 12x + 17](https://tex.z-dn.net/?f=%20-%201%20%20%2B%20%2014x%20%3D%2012x%20%2B%2017)
![14x - 1 = 12x + 17](https://tex.z-dn.net/?f=14x%20-%201%20%3D%2012x%20%2B%2017)
Add sides 1
![14x - 1 + 1 =12x + 17 + 1](https://tex.z-dn.net/?f=14x%20-%201%20%2B%201%20%3D12x%20%2B%2017%20%2B%201)
![14x = 12x + 18](https://tex.z-dn.net/?f=14x%20%3D%2012x%20%2B%2018)
Subtract sides 12x
![- 12x + 14x = - 12x + 12x + 18 \\](https://tex.z-dn.net/?f=%20-%2012x%20%2B%2014x%20%3D%20%20-%2012x%20%2B%2012x%20%2B%2018%20%5C%5C%20)
![2x = 18](https://tex.z-dn.net/?f=2x%20%3D%2018)
Divide sides by 2
![\frac{2x}{2} = \frac{18}{2} \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B2x%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B18%7D%7B2%7D%20%20%5C%5C%20)
![x = 9](https://tex.z-dn.net/?f=x%20%3D%209)
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CHECK :
![14(9) - 1 = 12(9) + 17](https://tex.z-dn.net/?f=14%289%29%20-%201%20%3D%2012%289%29%20%2B%2017)
![126 - 1 = 108 + 17](https://tex.z-dn.net/?f=126%20-%201%20%3D%20108%20%2B%2017)
![125 = 125](https://tex.z-dn.net/?f=125%20%3D%20125)
Thus the solution is correct .
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