now, if we take 2000 to be the 100%, what is 2200? well, 2200 is just 100% + 10%, namely 110%, and if we change that percent format to a decimal, we simply divide it by 100, thus 
.
so, 1.1 is the decimal number we multiply a term to get the next term, namely 1.1 is the common ratio.
![\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\a_1=2000\\r=1.1\\n=4\end{cases}\\\\\\S_4=2000\left[ \cfrac{1-(1.1)^4}{1-1.1} \right]\implies S_4=2000\left(\cfrac{-0.4641}{-0.1} \right)\\\\\\S_4=2000(4.641)\implies S_4=9282](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bsum%20of%20a%20finite%20geometric%20sequence%7D%5C%5C%5C%5CS_n%3D%5Csum%5Climits_%7Bi%3D1%7D%5E%7Bn%7D%5C%20a_1%5Ccdot%20r%5E%7Bi-1%7D%5Cimplies%20S_n%3Da_1%5Cleft%28%20%5Ccfrac%7B1-r%5En%7D%7B1-r%7D%20%5Cright%29%5Cquad%20%5Cbegin%7Bcases%7Dn%3Dn%5E%7Bth%7D%5C%20term%5C%5Ca_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5Cr%3D%5Ctextit%7Bcommon%20ratio%7D%5C%5C----------%5C%5Ca_1%3D2000%5C%5Cr%3D1.1%5C%5Cn%3D4%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5CS_4%3D2000%5Cleft%5B%20%5Ccfrac%7B1-%281.1%29%5E4%7D%7B1-1.1%7D%20%5Cright%5D%5Cimplies%20S_4%3D2000%5Cleft%28%5Ccfrac%7B-0.4641%7D%7B-0.1%7D%20%20%5Cright%29%5C%5C%5C%5C%5C%5CS_4%3D2000%284.641%29%5Cimplies%20S_4%3D9282%20)
Answer and Step-by-step explanation:
To solve, we would set the first number to x, and make an equation.
<u>Solve for x.</u>
x + (x - 6) + 3x = 69.
<u>Add and combine like terms.</u>
2x + 3x - 6 = 69
5x - 6 = 69
<u>Add 6 to each side of the equation.</u>
5x = 75
Divide by 5 to both sides.
x = 15
<u>The first number is 15.</u>
<u>The second number is (x - 6) = (15 - 6) = 9.</u>
<u>The third number is 3x = 3(15) = 45.</u>
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<em><u>#teamtrees #PAW (Plant And Water)</u></em>
Answer:
Median is 18, because 18 is the middle number.
Step-by-step explanation:
Answer:
x < -15
Step-by-step explanation:
-1x + 5 < 20
- 5 - 5
-1x < 15
/-1 /-1
x < -15
Answer:
Option B, 24 feet
Step-by-step explanation:
<u>Step 1: Determine the perimeter</u>
To find how much fence we will need to go around the garden means that we need to find the perimeter. In order to find the perimeter we need to add up all of the sides which we can do using the formula below.
Answer: Option B, 24 feet
