An arithmetic sequence can be expressed as explicitly or recursively
The explicit formula of the sequence is ![a_n = 11 - 4n](https://tex.z-dn.net/?f=a_n%20%3D%2011%20-%204n)
<h3>How to determine the explicit formula</h3>
The recursive formula is given as:
![a_n = a_{n -1} - 4](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn%20-1%7D%20-%204)
![a_1 = 7](https://tex.z-dn.net/?f=a_1%20%3D%207)
Substitute 2 for n in ![a_n = a_{n -1} - 4](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn%20-1%7D%20-%204)
![a_2 =a_1 - 4](https://tex.z-dn.net/?f=a_2%20%3Da_1%20-%204)
This gives
![a_2 =7 - 4](https://tex.z-dn.net/?f=a_2%20%3D7%20-%204)
![a_2 =3](https://tex.z-dn.net/?f=a_2%20%3D3)
Calculate the common difference (d)
![d = a_2 -a_1](https://tex.z-dn.net/?f=d%20%3D%20a_2%20-a_1)
![d = 3- 7](https://tex.z-dn.net/?f=d%20%3D%203-%207)
![d = -4](https://tex.z-dn.net/?f=d%20%3D%20-4)
The explicit formula is then calculated as:
![a_n = a_1 + (n - 1)d](https://tex.z-dn.net/?f=a_n%20%3D%20a_1%20%2B%20%28n%20-%201%29d)
This gives
![a_n = 7+ (n - 1)*-4](https://tex.z-dn.net/?f=a_n%20%3D%207%2B%20%28n%20-%201%29%2A-4)
Expand
![a_n = 7+4 - 4n](https://tex.z-dn.net/?f=a_n%20%3D%207%2B4%20-%204n)
![a_n = 11 - 4n](https://tex.z-dn.net/?f=a_n%20%3D%2011%20-%204n)
Hence, the explicit formula of the sequence is ![a_n = 11 - 4n](https://tex.z-dn.net/?f=a_n%20%3D%2011%20-%204n)
Read more about arithmetic sequence at:
brainly.com/question/6561461