Chapter 11.1, Problem 53PPS

To determine

Find the thickness of the paper after 37 fold.

Answer to Problem 53PPS

About 13,744 km

Explanation of Solution

Given:

When a piece of paper is folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, how thick would it be?

Concept Used:

The first term: $a_1=0.1\text{mm}$

Folded 37 times, so we need to find the 38^th term of the geometric sequence.

Common ratio: $\text{r = 2}$

General for of Geometric sequence: $a_n=a_1·{(r)}^{(n-1)}$

Calculation:

General for of Geometric sequence: $a_n=a_1·{(r)}^{(n-1)}$

  $a_1=0.1\text{mm ; r = 2 and n = 38}$

Now find the 38^th term: $a_{38}=0.1·{(2)}^{(38-1)}=13,744\text{km}$

Thus, the thickness of the paper after 37 fold is about 13,744 km.