Question

Frank has a sheet of paper which is 1/624 inch thick. If the sheet is folded in half, the total thickness will be 1/312 inch A second fold will produce a total thickness of 1/156 inch. What will be the thickness of the sheet if Frank folds it 8 times?

Answer 1

Answer:

The thickness of the sheet will be 16/39 inch after folded 8 times

Step-by-step explanation:

* Lets explain how to solve the problem

- Frank has a sheet of paper of 1/624 inch thick

- The sheet is folded in half, the total thickness is 1/312 inch

- The sheet folded in half again and the total thickness is 1/156 inch

- We need to know the thickness of the sheet after folded 8 times

∵ The 1st thickness is 1/624 inches

∵ The 2nd thickness is 1/312 inch ⇒ after 1st fold

∵ The 3rd thickness is 1/156 inch⇒ after 2nd fold

∵ 1/312 ÷ 1/624 = 2

∵ 1/156 ÷ 1/312 = 2

∴ There is a common ratio 2 between each two fold

∴ The thicknesses of the sheet after each fold formed a

   geometric series

∵ Any term of the geometric series is $a_{n}=a(r)^{n-1}$, where

  a is the first term, r is the ratio between each two consecutive

  terms and n is the position of the term

∵ a = 1/312 because it is the thickness of the 1st fold

∵ r = 2 , n = 8

∴ $a_{8}=\frac{1}{312}(2)^{8-1}=\frac{16}{39}$

∴ The thickness of the sheet will be 16/39 inch after fold 8 times

Answer 2

Answer:0.41 in

Step-by-step explanation: