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 [tex]a_{n}=a(r)^{n-1}[/tex], 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
∴ [tex]a_{8}=\frac{1}{312}(2)^{8-1}=\frac{16}{39}[/tex]
∴ The thickness of the sheet will be 16/39 inch after fold 8 times
