Answer:
an = 1/4(8)^n-1
Step-by-step explanation:
Given the following in a geometric sequence, a2=2, a3=16, and a4=128.
nth term of a sequence = ar^n-1
a is the first term
r is the common ratio
r = a3/a2 = a4/a3
r = 16/2 = 128/16
r = 8
a2 = ar
2 = 8a
a = 2/8
a = 1/4
The nth term by substituting the parameters will be;
an = 1/4(8)^n-1
Answer:
Right Triangles
Step-by-step explanation:
Answer:
![\frac{1}{9}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B9%7D%20)
Step-by-step explanation:
Let the numbers be x,y, where x>y
The geometric mean is
![\sqrt{xy}](https://tex.z-dn.net/?f=%20%5Csqrt%7Bxy%7D%20)
The Arithmetic mean is
![\frac{x + y}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%20)
The ratio of the geometric mean and arithmetic mean of two numbers is 3:5.
![\frac{ \sqrt{xy} }{ \frac{x + y}{2} } = \frac{3}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7Bxy%7D%20%7D%7B%20%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%20%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B5%7D%20)
We can write the equation;
![\sqrt{xy} = 3](https://tex.z-dn.net/?f=%20%5Csqrt%7Bxy%7D%20%20%3D%203%20)
or
![xy = 9 - - - (2)](https://tex.z-dn.net/?f=xy%20%3D%209%20-%20%20-%20%20-%20%282%29)
l
and
![\frac{x + y}{2} = 5](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%20%20%3D%205)
or
![x + y = 10 - - - (2)](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2010%20-%20%20-%20%20-%20%282%29)
Make y the subject in equation 2
![y = 10 - x - - - (3)](https://tex.z-dn.net/?f=y%20%3D%2010%20-%20x%20-%20%20-%20%20-%20%283%29)
Put equation 3 in 1
![x(10 - x) = 9](https://tex.z-dn.net/?f=x%2810%20-%20x%29%20%3D%209)
![10x - {x}^{2} = 9](https://tex.z-dn.net/?f=10x%20-%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%209)
![{x}^{2} - 10x + 9 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%2010x%20%2B%209%20%3D%200)
![(x - 9)(x - 1) = 0](https://tex.z-dn.net/?f=%28x%20-%209%29%28x%20-%201%29%20%3D%200)
![x =1 \: or \: 9](https://tex.z-dn.net/?f=x%20%3D1%20%20%5C%3A%20or%20%5C%3A%209)
When x=1, y=10-1=9
When x=9, y=10-9=1
Therefore x=9, and y=1
The ratio of the smaller number to the larger number is
![\frac{1}{9}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B9%7D%20)
Answer:
2.5, 16,3,32
Step-by-step explanation: