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.

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:

square units

= 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

common ratio r = 0.5

We have to find the 5th term of this sequence

Explicit formula of a geometric sequence is represented by

Now      

                   = (0.5)⁴

                   = 0.0625 in²

After 5 tears area would be  0.0625 in²

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step-by-step explanation: