Answer:
[tex]Area = \frac{1}{16}[/tex] 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:
[tex]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}[/tex]
[tex]a_5 = \frac{1}{16}[/tex] square units
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 [tex]\frac{T_{2} }{T_{1}}= \frac{0.5}{1}=0.5[/tex]
common ratio r = 0.5
We have to find the 5th term of this sequence
Explicit formula of a geometric sequence is represented by
[tex]T_{n} =a(r)^{n-1}[/tex]
Now [tex]T_{5} =1(0.5)^{5-1}[/tex]
= (0.5)⁴
= 0.0625 in²
After 5 tears area would be 0.0625 in²
