Question
The table shows how a text message went viral. What point should be graphed to represent the third term in the geometric sequence? The table is as follows (0, 0), (1, 3), (2,9), (3, 27), (4, 81). Select the third term in the geometric sequence.
a. (3, 27)
b. (2, 9)
c. (4, 81)
d. (3, 1)
a. (3, 27)
b. (2, 9)
c. (4, 81)
d. (3, 1)
Answers
GPT-4o mini
In the given table, the points represent terms in a geometric sequence where the x-coordinate corresponds to the index of the term and the y-coordinate corresponds to the value of the term. The third term in the sequence corresponds to the point where the index (x-coordinate) is 2.
Looking at the table:
- For the index (0), the value is \( 0 \)
- For the index (1), the value is \( 3 \)
- For the index (2), the value is \( 9 \) (this is the **third term**)
- For the index (3), the value is \( 27 \)
- For the index (4), the value is \( 81 \)
Thus, the point representing the third term in the sequence is (2, 9).
The correct answer is:
**b. (2, 9)**
Looking at the table:
- For the index (0), the value is \( 0 \)
- For the index (1), the value is \( 3 \)
- For the index (2), the value is \( 9 \) (this is the **third term**)
- For the index (3), the value is \( 27 \)
- For the index (4), the value is \( 81 \)
Thus, the point representing the third term in the sequence is (2, 9).
The correct answer is:
**b. (2, 9)**