SOLUTION: A rose garden has 21 bushes in one row, 17 bushes in the next row, then 13, and so on. If there are 66 bushes in the garden, in how many rows are they planted?

Algebra ->  Sequences-and-series -> SOLUTION: A rose garden has 21 bushes in one row, 17 bushes in the next row, then 13, and so on. If there are 66 bushes in the garden, in how many rows are they planted?       Log On


   

Question 379646: A rose garden has 21 bushes in one row, 17 bushes in the next row, then 13, and so on. If there are 66 bushes in the garden, in how many rows are they planted?


Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Aritmetic sequence:
c=a[1]-d
c=21-(-4)=25
.
a[n]=dn+c
a[n]=-4n+25
.
(n/2)(a[1]+a[n])=S[n]
(n/2)(21-4n+25)=66
n(46-4n)=132
46n-4n^2=132
4n^2-46n+132=0
2n^2-23n+66=0
(n-6)(2n-11)=0
n=6 rows
.
Ed