Question

question content area top part 1 a sheet of paper is cut into 6 ​same-size parts. each of the parts is then cut into 6 ​same-size parts and so on. a. after the 4th ​cut, how many of the smallest pieces of paper are​ there? b. after the nth​ cut, how many of the smallest pieces of paper are​ there?

Answer 1

After the 4th cut, we will have 1,296 pieces and after the nth cut, we will have $6^{n}$ pieces.

Here, we are given that a sheet of paper is cut into 6 ​same-size parts. Each of the parts is then cut into 6 ​same-size parts and so on.

Thus, after one cut we will have 6 pieces

After second cut, we will have 6*6 = 36 pieces

After the third cut, we will have 36*6 = 216 pieces

After the fourth cut, we will have 216*6 = 1,296 pieces

Now, we can clearly see a pattern here. The number of pieces follow a geometric progression with a common ratio of 6.

Thus, after the nth cut, the number of pieces will be-

a$r^{n-1}$

where a = first term which is 6

and r = common ratio which is also 6

⇒ 6*$6^{n-1}$

= $6^{n}$

Thus, after the 4th cut, we will have 1,296 pieces and after the nth cut, we will have $6^{n}$ pieces.

Learn more about geometric progression here-

https://brainly.com/question/24643676

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