Answer:
Factor the numerator and denominator and cancel the common factors.
1
Step-by-step explanation:
Hope this helps! Have a nice day!
The function A(n) = 22(1.1)^n-1 is an illustration of a geometric series
The sum of the 23rd through 40th terms of the series is 17.49
<h3>How to determine the sum of the
series</h3>
The nth term of the geometric series is given as:
![A(n) = 22(1.1)^{n-1](https://tex.z-dn.net/?f=A%28n%29%20%3D%2022%281.1%29%5E%7Bn-1)
The nth term of a series is represented as:
![A(n) = ar^{n-1](https://tex.z-dn.net/?f=A%28n%29%20%3D%20ar%5E%7Bn-1)
So, by comparison;
We have:
![a = 22](https://tex.z-dn.net/?f=a%20%3D%2022)
![r = 1.1](https://tex.z-dn.net/?f=r%20%3D%201.1)
The sum of nth term of a geometric progression is:
![S_n = \frac{a(r^n - 1)}{r - 1}](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Ba%28r%5En%20-%201%29%7D%7Br%20-%201%7D)
Start by calculating the sum of the first 22 terms
![S_{22} = \frac{22(1.1^{22} - 1)}{22 - 1}](https://tex.z-dn.net/?f=S_%7B22%7D%20%3D%20%5Cfrac%7B22%281.1%5E%7B22%7D%20-%201%29%7D%7B22%20-%201%7D)
![S_{22} = \frac{157.086}{21}](https://tex.z-dn.net/?f=S_%7B22%7D%20%3D%20%5Cfrac%7B157.086%7D%7B21%7D)
![S_{22} = 7.48](https://tex.z-dn.net/?f=S_%7B22%7D%20%3D%207.48)
Next, calculate the sum of the first 40 terms
![S_{40} = \frac{22(1.1^{40} - 1)}{40 - 1}](https://tex.z-dn.net/?f=S_%7B40%7D%20%3D%20%5Cfrac%7B22%281.1%5E%7B40%7D%20-%201%29%7D%7B40%20-%201%7D)
![S_{40} = \frac{973.70}{39}](https://tex.z-dn.net/?f=S_%7B40%7D%20%3D%20%5Cfrac%7B973.70%7D%7B39%7D)
![S_{40} = 24.97](https://tex.z-dn.net/?f=S_%7B40%7D%20%3D%2024.97)
Subtract S22 from S40
![S_{40} - S_{22} = 24.97 - 7.48](https://tex.z-dn.net/?f=S_%7B40%7D%20-%20S_%7B22%7D%20%3D%2024.97%20-%207.48)
![S_{40} - S_{22} = 17.49](https://tex.z-dn.net/?f=S_%7B40%7D%20-%20S_%7B22%7D%20%3D%2017.49)
Hence, the sum of the 23rd through 40th terms of the series is 17.49
Read more about progression at:
brainly.com/question/12006112
Answer:
1 point, (1.5,0)
Step-by-step explanation:
Inputting the equation into a graphing calculator (desmos) you can find the x intercept (where the line hits the x-axis)
Answer:
k = ![\frac{5}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D)
Step-by-step explanation:
Consider the scale factor (k) from T to T', that is the ratio of corresponding sides.
k =
=
= ![\frac{5}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D)