SOLUTION: The sum of ten numbers in an arithmetic progression (sequence) is 190. The sum of the fourth and eighth term exceeds the fifth term by 25. Find the first four terms of the sequence

Algebra ->  Sequences-and-series -> SOLUTION: The sum of ten numbers in an arithmetic progression (sequence) is 190. The sum of the fourth and eighth term exceeds the fifth term by 25. Find the first four terms of the sequence      Log On


   

Question 1076392: The sum of ten numbers in an arithmetic progression (sequence) is 190. The sum of the fourth and eighth term exceeds the fifth term by 25. Find the first four terms of the sequence. Only an algebraic solution will be accepted.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
First term, a.
common difference, d.

General term: a%2Bd%28n-1%29

Tenth term, a%2Bd%2810-1%29=a%2B9d.
Sum of the ten terms is 190: %28a%2Ba%2B9d%29%2810%2F2%29=190
5%282a%2B9d%29=190
2a%2B9d=38


The sum of the fourth and eighth term exceeds the fifth term by 25.
%28a%2Bd%284-1%29%29%2B%28a%2Bd%288-1%29%29-%28a%2Bd%285-1%29%29=25
-
a%2B3d%2Ba%2B7d-a-4d=25
a%2B6d=25

Solve this system for first term, a, and common difference, d:
system%282a%2B9d=38%2Ca%2B6d=25%29
You should be able to do that and find the first four terms.