Question

Visualize the following procedure: Tear in half a square piece of paper with an area of one square unit. Then tear it in half again. Predict the area of one of the resulting rectangles after 5 tears.

Answer 1

Answer:

= 0.0625 in²

Step-by-step explanation:

Area of a piece of paper = 1 unit²

then we tear this paper into half.

So area becomes 0.5 unit²

In this way the sequence formed will be

1, 0.5, 0.25, .........

This sequence is a geometric sequence

as $\frac{T_{2} }{T_{1}}= \frac{0.5}{1}=0.5$

common ratio r = 0.5

We have to find the 5th term of this sequence

Explicit formula of a geometric sequence is represented by

             $T_{n} =a(r)^{n-1}$

Now      $T_{5} =1(0.5)^{5-1}$

                   = (0.5)⁴

                   = 0.0625 in²

After 5 tears area would be  0.0625 in²

Answer 2

Answer:

$Area = \frac{1}{16}$ square units

Step-by-step explanation:

To predict the area of the piece of paper after 5 tears we can use a geometric sequence.

Each time a piece is torn, half of the previous area is lost. If the area of the first piece is 1 square unit then:

$a_1 = 1\\\\r = \frac{1}{2}\\\\a_2 = 1 *\frac{1}{2}\\\\a_2 = \frac{1}{2}\\\\a_n = 1(\frac{1}{2})^{n-1}\\\\a_5 = 1(\frac{1}{2})^{5-1}$

$a_5 = \frac{1}{16}$ square units