SOLUTION: Find the sum of the first twenty terms of the arithmetic sequence given that the tenth term is 39 and the sum of the ten terms is 165

Algebra ->  Sequences-and-series -> SOLUTION: Find the sum of the first twenty terms of the arithmetic sequence given that the tenth term is 39 and the sum of the ten terms is 165       Log On


   

Question 1089974: Find the sum of the first twenty terms of the arithmetic sequence given that the tenth term is 39 and the sum of the ten terms is 165
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B10%5D=39
and
S%5B10%5D=165
.
.
.
You know that,
S%5Bn%5D=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29
Substituting,
%2810%2F2%29%28a%5B1%5D%2B39%29=165
a%5B1%5D%2B39=33
a%5B1%5D=-6
and
a%5B10%5D=a%5B1%5D%2B%2810-1%29d
39=-6%2B9d
9d=45
d=5
So,
a%5B20%5D=-6%2B19%285%29
a%5B20%5D=-6%2B95
a%5B20%5D=89
and,
S%5B20%5D=%2820%2F2%29%28-6%2B89%29
S%5B20%5D=10%2883%29
S%5B20%5D=830