your class is conducting an experiment to study geometric sequences. The class forms a line. the first person takes a whole pizza,divides it in half, keeps half, and hands it to the next person. The next people in line do the same with there peices. Which portion does the seventh person in line get
A)1/256
B)1/64
C)1/128
D)1/32
how do you solve this?
If the first person get 1/2
And you said it is a geometric sequence
The second person gets
1/4
The third 1/8
1/2,1/4,1/8..........T7
a=1/2
T7=ar^(n-1)=1/2(1/2)^6=(1/2)^7=1/128
To solve this problem, we need to understand the pattern of the geometric sequence.
In this experiment, each person takes half of the pizza they receive and hands the other half to the next person in line. So, the portion each person receives will be half the size of the portion the previous person received.
To find the portion the seventh person receives, we can start with the size of the first person's portion and repeatedly halve it until we reach the seventh person.
Let's break down the portions received by each person:
1st person: Whole pizza, which is 1/1 or 1.
2nd person: Receives half of what the 1st person had. So, it is 1/2 or 1/2.
3rd person: Receives half of what the 2nd person had. So, it is (1/2) * (1/2) or 1/4.
4th person: Receives half of what the 3rd person had. So, it is (1/4) * (1/2) or 1/8.
5th person: Receives half of what the 4th person had. So, it is (1/8) * (1/2) or 1/16.
6th person: Receives half of what the 5th person had. So, it is (1/16) * (1/2) or 1/32.
7th person: Receives half of what the 6th person had. So, it is (1/32) * (1/2) or 1/64.
Therefore, the portion the seventh person in line receives is 1/64.
So, the correct answer is option B) 1/64.