Given:
Given the series
![\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+\frac{1}{40}+...](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%2B%5Cfrac%7B1%7D%7B10%7D%2B%5Cfrac%7B1%7D%7B20%7D%2B%5Cfrac%7B1%7D%7B40%7D%2B...)
Required: Identify the following series as geometric or arithmetic. Also identify the series as infinite or finite.
Explanation:
The given series is a geometric series as the terms of the series are 1/2 times its previous term.
![\begin{gathered} a_2=\frac{1}{10}=\frac{1}{2}\cdot\frac{1}{5}=\frac{1}{2}a_1 \\ a_3=\frac{1}{20}=\frac{1}{2}\cdot\frac{1}{10}=\frac{1}{2}a_2 \\ a_4=\frac{1}{40}=\frac{1}{2}\cdot\frac{1}{20}=\frac{1}{2}a_3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a_2%3D%5Cfrac%7B1%7D%7B10%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%5Cfrac%7B1%7D%7B5%7D%3D%5Cfrac%7B1%7D%7B2%7Da_1%20%5C%5C%20a_3%3D%5Cfrac%7B1%7D%7B20%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%5Cfrac%7B1%7D%7B10%7D%3D%5Cfrac%7B1%7D%7B2%7Da_2%20%5C%5C%20a_4%3D%5Cfrac%7B1%7D%7B40%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%5Cfrac%7B1%7D%7B20%7D%3D%5Cfrac%7B1%7D%7B2%7Da_3%20%5Cend%7Bgathered%7D)
So, the given series is a geometric series with first term, a = 1/5 and common difference, d = 1/2.
The three dots at the end of the series means the series is continuing. So, it is an infinite series.
Final Answer: The given series is an infinite geometric series.
Answer:
72 animals
Step-by-step explanation:
Let d = dogs
d+d25% = cats
Changing to decimal form
d+.25d= cats
d(1.25) =cats
There are 40 cats
d(1.25) =40
Divide each side by 1.25
1.25d/1.25 = 40/1.25
d =32
There are 32 dogs and 40 cats
The total number of animals
32+40 = 72
No, it is not a solution, as 15 is not less-than fifteen.<span />
You mean V=πr2h or is there a longer one that I am not aware of?