Answer:
59049
Step-by-step explanation:
Answer:
ill help
Step-by-step explanation:
Answer:
![a_n = 16(\frac{1}{4})^{n - 1}](https://tex.z-dn.net/?f=%20a_n%20%3D%2016%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bn%20-%201%7D%20)
Step-by-step explanation:
Given:
Fifth term of a geometric sequence = ![\frac{1}{16}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B16%7D%20)
Common ratio (r) = ¼
Required:
Formula for the nth term of the geometric sequence
Solution:
Step 1: find the first term of the sequence
Formula for nth term of a geometric sequence =
, where:
a = first term
r = common ratio = ¼
Thus, we are given the 5th term to be ¹/16, so n here = 5.
Input all these values into the formula to find a, the first term.
![\frac{1}{16} = a*\frac{1}{4}^{5 - 1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B16%7D%20%3D%20a%2A%5Cfrac%7B1%7D%7B4%7D%5E%7B5%20-%201%7D%20)
![\frac{1}{16} = a*\frac{1}{4}^{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B16%7D%20%3D%20a%2A%5Cfrac%7B1%7D%7B4%7D%5E%7B4%7D%20)
![\frac{1}{16} = a*\frac{1}{256}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B16%7D%20%3D%20a%2A%5Cfrac%7B1%7D%7B256%7D%20)
![\frac{1}{16} = \frac{a}{256}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B16%7D%20%3D%20%5Cfrac%7Ba%7D%7B256%7D%20)
Cross multiply
![1*256 = a*16](https://tex.z-dn.net/?f=%201%2A256%20%3D%20a%2A16%20)
Divide both sides by 16
![\frac{256}{16} = \frac{16a}{16}](https://tex.z-dn.net/?f=%20%5Cfrac%7B256%7D%7B16%7D%20%3D%20%5Cfrac%7B16a%7D%7B16%7D%20)
![16 = a](https://tex.z-dn.net/?f=%2016%20%3D%20a%20)
![a = 16](https://tex.z-dn.net/?f=%20a%20%3D%2016%20)
Step 2: input the value of a and r to find the nth term formula of the sequence
nth term = ![ar^{n - 1}](https://tex.z-dn.net/?f=%20ar%5E%7Bn%20-%201%7D%20)
nth term = ![16*\frac{1}{4}^{n - 1}](https://tex.z-dn.net/?f=%2016%2A%5Cfrac%7B1%7D%7B4%7D%5E%7Bn%20-%201%7D%20)
![a_n = 16(\frac{1}{4})^{n - 1}](https://tex.z-dn.net/?f=%20a_n%20%3D%2016%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bn%20-%201%7D%20)
Answer:
its 84 but tysm thats so sweet
Step-by-step explanation:
Answer:
From least to greatest
23* 1/4, 23* 2/2, 23* 13/5
Explanation
In order to do this without multiplication, place the fractions in ascending order.
The denominators of these fractions have 20 as a common multiple.
2/2 • 10 = 20/20
1/4 • 5 = 5/20
13/5 • 4 = 52/20
From this it logically follows that the fractions in ascending order are:
1/4, 2/2, 13/5
Therefore the products in ascending order are:
23* 1/4, 23* 2/2, 23* 13/5