Asheet of paper is cut into 2 same-size parts. each of the parts is then cut into 2 same-size parts and so on. a. after the 7th 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?

a) 128 b) 512

Step-by-step explanation:

The key to solve this, is to think of it as a Geometric Sequence. Since, there is a constant ratio (q), each time the sheet of paper is cut, it is divided into two pieces or 1/2.

If after the 1st cut there are two pieces i.e. 1/2

a) After the 7th cut, how many of the smallest pieces of paper are there?

You can either count the sequence above: 1/128 then 128 pieces or apply the recursive formula for any Term of a Geometric Sequence;

The Denominator indicates the smallest pieces of paper: 128

b)  After the 9th cut, how many of the smallest pieces of paper are there?

Similarly to the item a: 1/512 then 512

The Denominator indicates the smallest pieces of paper after the Ninth cut: 512

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step-by-step explanation:

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.