SOLUTION: In the arithmetic sequence, the 3rd term is 4 and the 8th term is 49. Find the 1st term, the common difference and the sum of the first ten terms.

Algebra ->  Sequences-and-series -> SOLUTION: In the arithmetic sequence, the 3rd term is 4 and the 8th term is 49. Find the 1st term, the common difference and the sum of the first ten terms.       Log On


   

Question 484324: In the arithmetic sequence, the 3rd term is 4 and the 8th term is 49. Find the 1st term, the common difference and the sum of the first ten terms.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
In the arithmetic sequence, the 3rd term is 4 and the 8th term is 49. Find the 1st term, the common difference and the sum of the first ten terms.
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

>>...the 3rd term is 4...<<

a%5B3%5D=a%5B1%5D%2B%283-1%29d
4=a%5B1%5D%2B2d
a%5B1%5D%2B2d=4


>>...the 8th term is 49...<<

a%5B8%5D=a%5B1%5D%2B%288-1%29d
49=a%5B1%5D%2B7d
a%5B1%5D%2B7d=49


So we have a system of equations:

system%28a%5B1%5D%2B2d=4%2Ca%5B1%5D%2B7d=49%29

Solve by substitution or elimination and get

a%5B1%5D=-14 and d=9

first term is -14,

Here is the sequence to 10 terms:

-14, -5, 4, 13, 22, 31, 40, 49, 58, 67 

To get the sum of the first 10 terms, 
we use the formula:

S%5Bn%5D+=+expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29

S%5B10%5D+=+expr%2810%2F2%29%282%28-14%29%2B%2810-1%299%29

S%5B10%5D+=+5%28-28%2B%289%299%29

S%5B10%5D+=+5%28-28%2B81%29

S%5B10%5D+=+5%2853%29

S%5B10%5D+=+265

sum =  265

Edwin