Question

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

Question 2 options:


14.001 in.


0.41 in.


0.205 in.


128 in.

Answer 1

0.41 in.

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
`a_(n)=a(r)^(n-1)`

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

`a_(8)=(1)/(312)(2)^(8-1)=(16)/(39)`=> 0.41 in