Question

a grocer stacks apples in a pyramid-like stack whose rectangular base is 6 apples by 6 apples. Each aplle aboce the first level rests in a pocket formed by four apples below. The stack is completed by single row of apples. how many apples are in the stack

Answer 1

Answer:

The number of apples in each layer are called "triangular" numbers, that is,

1, 3, 6, 10, 15, ....

think of the balls in a game of billiards and the total if you rack them up.

So the number of apples in each layer working down from the top are

1, 3, 6, 10, 15, ....

they gave you the formula producing these numbers, e.g for level 4, k=4

and the number is 4(5)/2 = 10, the fourth number in my list

k(k+1)/2 = (k^2 + k)/2 or (1/2)k^2 + (1/2)k + 0

so for the given question, a = 1/2, b = 1/2, and c = 0

I anticipate the next question to be to find the number of apples for a given

number of layers.

Step-by-step explanation:

Answer 2

Answer: There are $90$ oranges in the stack

Given:

Figure in which oranges are stacked = Pyramid

Rectangular base $=6$×$6$

To find:

How many oranges are in the stack

Solution:

• Oranges in the first row $= 6$×$6=36$
• Oranges in the second row $=5$ ×$5=25$
• Oranges in the third row $=4$ × $4 = 16$
• Oranges in the fourth row $= 3$ × $3 = 9$
• Oranges in the fifth row  $=2$ × $2 = 4$

Therefore,

Total oranges

$= 36 + 25 + 16 + 9 + 4$

$= 90$

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