SOLUTION: The first term of an arithmetic sequence is 5. The ratio of the sum of the first four terms to the sum of the first ten terms is 8:35. Find the common difference.

Algebra ->  Sequences-and-series -> SOLUTION: The first term of an arithmetic sequence is 5. The ratio of the sum of the first four terms to the sum of the first ten terms is 8:35. Find the common difference.       Log On


   

Question 1146198: The first term of an arithmetic sequence is 5. The ratio of the sum of the first four terms to the sum of the first ten terms is 8:35. Find the common difference.
Answer by Edwin McCravy(20077) About Me  (Show Source):
You can put this solution on YOUR website!
<--sum of first n terms.
The first term of an arithmetic sequence is 5.
The ratio of the sum of the first four terms to the sum of the first ten terms is 8:35.
 

Sum of first four terms: 
                         matrix%281%2C3%2CS%5B4%5D%2C%22%22=%22%22%2C+2%2A%2810%2B3d%5E%22%22%29%29
                         matrix%281%2C3%2CS%5B4%5D%2C%22%22=%22%22%2C+20%2B6d%29%29

Sum of first ten terms: 
                         matrix%281%2C3%2CS%5B10%5D%2C%22%22=%22%22%2C+5%2A%2810%2B9d%5E%22%22%29%29
                         matrix%281%2C3%2CS%5B10%5D%2C%22%22=%22%22%2C+50%2B45d%29%29

Their ratio 

matrix%281%2C3%2C%2850%2B45d%29%2F%2820%2B6d%29%2C%22%22=%22%22%2C8%2F35%29%29


You solve that for d. Begin by cross-multiplying.

Edwin