SOLUTION: A large pile of soil is divided into 10 piles. One of these is further divided into 10 smaller​ piles, and so on. a. Assuming enough​ soil, can exactly 27 piles be

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Question 1040679: A large pile of soil is divided into 10 piles. One of these is further divided into 10 smaller​ piles, and so on.
a. Assuming enough​ soil, can exactly 27 piles be obtained this​ way?
b. What is the number of piles after the nth​ division?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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A large pile of soil is divided into 10 piles. One of these is further divided into 10 smaller piles, and so on.
a. Assuming enough soil, can exactly 27 piles be obtained this way?
b. What is the number of piles after the n-th division?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1-st step: 1 pile disappears, 10 added; (1 --->  1-1+10 = 10); the output is 10. Same as 9 add to 1.

2-nd step: of 10 piles 1 pile disappears, 10 added; (10 --->  10-1+10 = 19); the output is 19. Same as 9 add to 10.

3-rd step: of 19 piles 1 pile disappears, 10 added; (19 --->  19-1+10 = 28); the output is 28 piles. Same as 9 add to 19.


Observation/conclusion: every step adds 9 piles to the current amount of piles.


Arithmetic progression 1, 10, 19, 28, 37, . . .  with he first term 1 and the common difference 9.


27 never can be an output.

Solved.


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