Answer :
Answer:
0.41 in.
Step-by-step explanation:
Given:
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
Required: thickness of the sheet after folded 8 times=?
1st thickness= 1/624 inches
2nd thickness = 1/312 inch(after 1st fold)
3rd thickness=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 =first term
r = ratio between each two consecutive terms
n=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]=> 0.41 in