SOLUTION: Find n for a series for which a1=9, d=4.5, and Sn=40.5

Algebra ->  Test -> SOLUTION: Find n for a series for which a1=9, d=4.5, and Sn=40.5      Log On


   

Question 250532: Find n for a series for which a1=9, d=4.5, and Sn=40.5
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We have the nth term formula as
T(n) = a1 + d(n-1)
From this we have
T(n) = 9 + 4.5(n-1)
or
T(n) = 4.5n + 4.5
The sum of this is
SUM(n=1 to k) [4.5n + 4.5] is
4.5(k(k+1))/2 + 4.5k = 40.5
multiplying both sides by 2, we get
4.5k^2 + 4.5k + 9k = 81
4.5k^2 + 13.5k - 81 = 0.
By quadratic, we get
k = 3 or k = -6.
After 3 terms we get the sum of 40.5.