You're being asked to work out
.
How many terms do you think you're going to have?
i am totally confused about this practice problem. what steps are required i feel it's so overwhelming where do i start.
At a grocery store oranges are piled to form a pyramid shape. the person who stacks the fruit has found that 18 by 26 oranges will fit in the bottom row. each successive row can can fit one less orange in both the length and width. if this pattern continues, how many oranges will there be in the pyramid? (it is important you know how many rows the pyramid will have.)
Well, why don't you try it with a simpler example; say 4 by 6 in bottom row.
The next row will be 3 by 5, then 2 by 4, finally 1 by 3 at top : still with me?
So from top down, you have 3, 8, 15, 24 ; a total of 50, right?
Notice that these go up by 5, then 7, then 9.
Can you handle that with what you've learned?
If so, apply same strategy to your 18 by 26 case.
Hello, leafs50!
Your usual sequence/series formulas won't help you with this one.
We can simply crank out the answer . . . or derive a formula.
Neither method is pleasant.
At a grocery store, oranges are piled to form a pyramid shape.
The produce manager has found that 18 by 26 oranges will fit in the bottom level.
Each successive level can can fit one less orange in both the length and width.
If this pattern continues, how many oranges will there be in the pyramid?
The no-brainer method:
. .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
We can derive the formula, but it will take a while . . .
Reading from the top of the pyramid, we have these facts:
. .
The Totals form this sequence: .
Take the difference of consecutive terms,
. . then the differences of the differences, etc.
We see that the third differences are constant.
. . Hence, the generating function is of the third degree.
The general cubic function is: .
. . and we must determine
We know the first four terms of the sequence:
. .
Substitute into [8]: .
Substitute into [5]: .
Substitute into [1]: .
Hence, the generating function is: .
Therefore: .
. . and: .