SOLUTION: A total of $9,100 in prizes is awarded to the top 8 entries in a science project contest. The highest prize is $2,000. The differences between successive prizes are equal. What is

Algebra ->  Sequences-and-series -> SOLUTION: A total of $9,100 in prizes is awarded to the top 8 entries in a science project contest. The highest prize is $2,000. The differences between successive prizes are equal. What is      Log On


   

Question 695673: A total of $9,100 in prizes is awarded to the top 8 entries in a science project contest. The highest prize is $2,000. The differences between
successive prizes are equal. What is the amount, in dollars, of the lowest prize?
A. $200
B. $275
C. $425
D. $650
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the first n terms of an arithmetic sequence is
S%5Bn%5D+=+%28n%2F2%29%28a%5B1%5D+%2B+a%5Bn%5D%29
S%5B8%5D+=+%288%2F2%29%28a%5B1%5D+%2B+a%5B8%5D%29
9100+=+4%282000+%2B+a%5B8%5D%29, divide both sides by 4
2275+=+2000+%2B+a%5B8%5D
a%5B8%5D+=+275
The lowest prize is $275.