MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

Answer:The thickness of the sheet will be 16/39 inch after folded 8 timesStep-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