SOLUTION: A display of cans in a grocery store consists of 14 cans in the bottom row, 12 cans in the next row, and so on in an arithmetic sequence. The top row has 4 cans. Find the total num

Question 1175830: A display of cans in a grocery store consists of 14 cans in the bottom row, 12 cans in the next row, and so on in an arithmetic sequence. The top row has 4 cans. Find the total number of cans in the display.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Take the average (mean, half sum) of the 14 and 4, which is  =  = 9,


and mulriply it by the number of rows, which is   =  = 5+1 = 6.


This product  9*6 = 54 is your ANSWER

CHECK made with Excel.             14 + 12 + 10 + 8 + 6+ 4 = 54.             ! Precisely correct !

Solved.

...............

As you understand, this display of cans represents a trapezoid, if to consider its front view.

What we do, when we solve the problem, is changing the format of this trapezoid to RECTANGULAR front view,
rearranging the cans. You may think about the solution in this way . . .

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It is about finding sum of an arithmetic progression.

For introductory lessons on arithmetic progressions see
    - 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.

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