The answer should be 21 if I am not mistaken
The answer I believe is going to be 28.4
Step-by-step explanation:
4a(a-x)+x(a-x)
[4a]2-4ax+ax-(x)2
(4a)2-3ax-(x)2
The recursive formula for the geometric sequence is ![a_n=(-\frac{1}{4} )a_{n-1}](https://tex.z-dn.net/?f=a_n%3D%28-%5Cfrac%7B1%7D%7B4%7D%20%29a_%7Bn-1%7D)
Explanation:
The given sequence is ![\{-16,4,-1,........\}](https://tex.z-dn.net/?f=%5C%7B-16%2C4%2C-1%2C........%5C%7D)
We need to determine the recursive formula for the given geometric sequence.
To determine the recursive formula, first we shall find the common difference.
Since, it is a geometric sequence, the common difference can be determined by
![r=\frac{4}{-16} =-\frac{1}{4}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B-16%7D%20%3D-%5Cfrac%7B1%7D%7B4%7D)
![r=-\frac{1}{4}](https://tex.z-dn.net/?f=r%3D-%5Cfrac%7B1%7D%7B4%7D)
Hence, the common difference of the given geometric sequence is ![r=-\frac{1}{4}](https://tex.z-dn.net/?f=r%3D-%5Cfrac%7B1%7D%7B4%7D)
The recursive equation for the geometric sequence can be determined using the formula,
![a_n=r(a_{n-1})](https://tex.z-dn.net/?f=a_n%3Dr%28a_%7Bn-1%7D%29)
Substituting the value
, we get,
![a_n=(-\frac{1}{4} )a_{n-1}](https://tex.z-dn.net/?f=a_n%3D%28-%5Cfrac%7B1%7D%7B4%7D%20%29a_%7Bn-1%7D)
Thus, the recursive formula for the geometric sequence is ![a_n=(-\frac{1}{4} )a_{n-1}](https://tex.z-dn.net/?f=a_n%3D%28-%5Cfrac%7B1%7D%7B4%7D%20%29a_%7Bn-1%7D)
![-0.6](https://tex.z-dn.net/?f=-0.6)
For more help, Take a look at this chart.