Your class is conducting an experiment to study geometric sequence. The class forms a line. The first person takes a whole pizza, divided it in half, keeps half, and hands the other half to the next person. The next person in line do the same thing with their piece. Which portion of the whole pizza does the seventh person in line get?
A. 1/256
B. 1/64
C. 1/128
D. 1/32
you clearly have
a = 1/2
r = 1/2
You want the 7th term is thus
1/2 * (1/2)^6 = 1/2^7 = 1/128
And if the textbook wrote the problem exactly as you posted it, their editor should be shot.
To determine the portion of the whole pizza the seventh person in line gets, we need to understand that the division of the pizza results in a geometric sequence. Each person receives half the size of the previous person's portion.
Let's denote the size of the whole pizza as '1'.
The first person takes half of the pizza, which is 1/2.
The second person takes half of 1/2, which is (1/2) * (1/2) = 1/4.
The third person takes half of 1/4, which is (1/2) * (1/4) = 1/8.
The fourth person takes half of 1/8, which is (1/2) * (1/8) = 1/16.
The fifth person takes half of 1/16, which is (1/2) * (1/16) = 1/32.
The sixth person takes half of 1/32, which is (1/2) * (1/32) = 1/64.
Therefore, the seventh person in line will get half of what the sixth person received, which is (1/2) * (1/64) = 1/128.
Thus, the answer is C. 1/128.
To find out the portion of the whole pizza that the seventh person in line gets, we need to understand the pattern in which the pizza is divided. In this scenario, each person takes their portion, divides it in half, keeps one half, and passes the other half to the next person.
This process forms a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio (in this case, the common ratio is 1/2).
To determine the portion the seventh person receives, we can use the formula for a geometric sequence:
\[a_n = a_1 \cdot (r)^{n-1}\]
Where:
- \(a_n\) is the \(n\)th term in the sequence,
- \(a_1\) is the first term in the sequence,
- \(r\) is the common ratio,
- \(n\) is the position of the term we want to find.
In this case, the first person receives the entire pizza, so \(a_1 = 1\). The common ratio is 1/2 (since each slice is divided in half), and we want to find the portion received by the seventh person, so \(n = 7\).
Using the formula, we can substitute these values and solve for \(a_7\):
\[a_7 = 1 \cdot (1/2)^{7-1}\]
\[a_7 = 1 \cdot (1/2)^6\]
\[a_7 = 1/2^6\]
\[a_7 = 1/64\]
Therefore, the portion of the whole pizza that the seventh person in line receives is 1/64.
The correct answer is B. 1/64.