Answer:
|4| - 2 = 2
|4| - 6 = -2
Step-by-step explanation:
Sum of the First n Terms of a Geometric Sequence
Given a geometric sequence (or series) with a first-term a1 and common ratio r, the sum of the first n terms is given by:
![S_n=a_1\cdot\frac{1-r^n}{1-r}](https://tex.z-dn.net/?f=S_n%3Da_1%5Ccdot%5Cfrac%7B1-r%5En%7D%7B1-r%7D)
We are given the series:
![120-80+\frac{160}{3}-\frac{320}{9}+\cdots](https://tex.z-dn.net/?f=120-80%2B%5Cfrac%7B160%7D%7B3%7D-%5Cfrac%7B320%7D%7B9%7D%2B%5Ccdots)
Before calculating the required sum, we need to find the common ratio. It's defined as the division of two consecutive terms. For example, using the first two terms:
![\begin{gathered} r=-\frac{80}{120} \\ Simplify\colon \\ r=-\frac{2}{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20r%3D-%5Cfrac%7B80%7D%7B120%7D%20%5C%5C%20Simplify%5Ccolon%20%5C%5C%20r%3D-%5Cfrac%7B2%7D%7B3%7D%20%5Cend%7Bgathered%7D)
The first term is a1 =120. Now apply the formula:
![S_8=120\cdot\frac{1-(-\frac{2}{3})^8}{1+\frac{2}{3}}](https://tex.z-dn.net/?f=S_8%3D120%5Ccdot%5Cfrac%7B1-%28-%5Cfrac%7B2%7D%7B3%7D%29%5E8%7D%7B1%2B%5Cfrac%7B2%7D%7B3%7D%7D)
Operating:
![\begin{gathered} S_8=120\cdot\frac{1-\frac{2^8}{3^8}}{\frac{5}{3}} \\ S_8=120\cdot\frac{1-\frac{256}{6561}}{\frac{5}{3}} \\ S_8=120\cdot\frac{\frac{6561-256}{6561}}{\frac{5}{3}} \\ S_8=120\cdot\frac{\frac{6305}{6561}}{\frac{5}{3}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20S_8%3D120%5Ccdot%5Cfrac%7B1-%5Cfrac%7B2%5E8%7D%7B3%5E8%7D%7D%7B%5Cfrac%7B5%7D%7B3%7D%7D%20%5C%5C%20S_8%3D120%5Ccdot%5Cfrac%7B1-%5Cfrac%7B256%7D%7B6561%7D%7D%7B%5Cfrac%7B5%7D%7B3%7D%7D%20%5C%5C%20S_8%3D120%5Ccdot%5Cfrac%7B%5Cfrac%7B6561-256%7D%7B6561%7D%7D%7B%5Cfrac%7B5%7D%7B3%7D%7D%20%5C%5C%20S_8%3D120%5Ccdot%5Cfrac%7B%5Cfrac%7B6305%7D%7B6561%7D%7D%7B%5Cfrac%7B5%7D%7B3%7D%7D%20%5Cend%7Bgathered%7D)
Calculating:
The unit rate is how many miles per hour so if you divide, then you will get the number of miles traveled per hour.
Divide 426 by 7.
60.85714...is the answer
The unit rate is D.
Answer:
Step-by-step explanation:
v = πr²h = π·2²·3.5 = 14π cm³ ≅ 44 cm³
The answer would be -14<span>√2 or the decimal form is 19.79898987...</span>