Question

How to use geometry progession in this situation ?

A piece of rectangular paper can be folded in half by 12 times. Given that the thickness of the paper is 0.0075 cm

Find the fold of the paper fold when the paper folds half by 10 times

Answer 1

See below

Explanation:

After 1 fold the thickness is multiplied by `2=2^1`
After 2 fold idem by `4=2^2`
After 3 fold idem by `8=2^3`
After n fold idem by `2^n` this is a geometric sequence of common ratio 2 and first term 2 (if n=1)

Then after 10 fold we are multipliyed by `2^10`

This number is `2^10=1024`

Initial thickness is `0.0075xx2^10=0.0075xx1024=7.68 cm`

Once solved, think about this

Is the thickness double if we fold 20 times?. No

After 20 times the thickness is

`0.0075xx2^20=0.0075xx 1048576=7864.32 cm=78.6432 mts`!!!