SOLUTION: In an arithmetric progression the sum of the first 8 terms is 54 and the 6th term is 3 times the second term. I need to find the first term and the sum of the first 20 terms. I ha

Algebra ->  Sequences-and-series -> SOLUTION: In an arithmetric progression the sum of the first 8 terms is 54 and the 6th term is 3 times the second term. I need to find the first term and the sum of the first 20 terms. I ha      Log On


   

Question 328497: In an arithmetric progression the sum of the first 8 terms is 54 and the 6th term is 3 times the second term. I need to find the first term and the sum of the first 20 terms.
I have been over this question so many times any help would be gratefull thanks.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let f=first term and d=difference

"In an arithmetric progression the sum of the first 8 terms is 54" ___ 8f + 28d = 54
___ each successive term adds an "f" and some d's

"the 6th term is 3 times the second term" ___ f + 5d = 3(f + d) ___ f + 5d = 3f + 3d ___ 2d = 2f ___ d = f

substituting ___ 8f + 28(f) = 54 ___ f = 54/36 = 3/2

sum of the 1st 20 terms ___ 20f + 190d = 210(3/2) = 315