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 1107363: 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 ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
21 + 17 + 13 + 9 + 5 + 1 = 66.

6 rows.

Surely, one can use the formula for the sum of an arithmetic progression,

but it is too powerful tool for such simple problem.

Much faster way is to add the numbers directly (and mentally).


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Although, if you want to use well known formulas for arithmetic progression, you can do it.

On arithmetic progressions, see introductory lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.