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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.

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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.