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in a pyramid. he wants 1 bale of hay on the top. the second row down will have four bales. the third row will have nine bales. he wants pattern for eight rows.

HowHome many bales does he have to have 

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2 Answers

Paul's answer is certainly a good one, and correct; however, there is another way to look at this, in addition to the 1-squared (1x1), 2-squared (2x2), etc as Paul pointed out.  You could look at it as the number of units (bales of hay) each level increases by 1, 3, 5 (and continuing from Level 4-8), 7, 9, 11, 13, 15, 17; in other words, the bales are increasing by odd numbers.  The next level (4) will increase by 7; add 7 to the prior level total of 9 -- 7 + 9 = 16.  Add 9 to this total for the next level -- 9 + 16 = 25.  And so on. 


So, to answer your question - how many bales of hay does he have -- 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 = 204 total bales. 


Paul's way of looking at it is more concise, but it's always good to see the problems from different angles :)

The pyramid will 8 levels.

The 1st level is a 1x1 =1

The 2nd level is a 2x2=4

The 3rd level is a 3x3=9

And so on until the 8th level which would be 8x8 =64

Then add the total number from each level up to get a total for the whole pyramid.