- The first four terms are : 15000, 14850, 14700, 14550
- a = 15000 ; d = -150
- The explicit formula is :
![a_{n} = - 150n \: + 15150](https://tex.z-dn.net/?f=%20%20a_%7Bn%7D%20%3D%20%20-%20150n%20%5C%3A%20%20%2B%2015150)
The first term of the sequence, a = 15,000
Each subsequent winner gets $150 less
Hence, the common difference, d = - $150
The first four terms :
First term, a1 = $15000
Second term, a2 = a - d = $15000 - $150 = $14850
Third term, a3 = a2 - d = $14850 - $150 = $14700
Fourth term, a4 = a3 - d = $14700 - $150 = $14550
a, for the sequence is the first term = $15000
d, for the sequence is the common $150 (difference between successive wins).
Explicit formula for the general term :
![a_{n} \: = nd \: + c](https://tex.z-dn.net/?f=%20%20a_%7Bn%7D%20%5C%3A%20%20%3D%20nd%20%5C%3A%20%2B%20c%20)
For n = 1
![15000 = 1( - 150) + c](https://tex.z-dn.net/?f=%2015000%20%3D%201%28%20-%20150%29%20%20%2B%20c)
![15000 = - 150 + c](https://tex.z-dn.net/?f=15000%20%3D%20%20-%20150%20%2B%20c)
![c = 15150](https://tex.z-dn.net/?f=c%20%3D%2015150)
Hence, the explicit formula for the nth term is :
![a_{n} \: = - 150n \: + 15150](https://tex.z-dn.net/?f=%20a_%7Bn%7D%20%5C%3A%20%20%3D%20%20-%20150n%20%5C%3A%20%20%2B%2015150)
Learn more : brainly.com/question/12006170