Write the first five terms of the geometric sequence whose first term is negative 1​, and whose common ratio is 3.

Question

Question content area bottom
Part 1
a 1equals
  
enter your response here

Answer 1

To generate the first five terms of a geometric sequence, we start with the first term \( a_1 \) and multiply each term by the common ratio \( r \).

Given:

• First term \( a_1 = -1 \)
• Common ratio \( r = 3 \)

The formula for the \( n \)-th term of a geometric sequence is: \[ a_n = a_1 \cdot r^{(n-1)} \]

Now, we can calculate the first five terms:

1. First term:
   \[ a_1 = -1 \]

2. Second term:
   \[ a_2 = a_1 \cdot r = -1 \cdot 3 = -3 \]

3. Third term:
   \[ a_3 = a_1 \cdot r^2 = -1 \cdot 3^2 = -1 \cdot 9 = -9 \]

4. Fourth term:
   \[ a_4 = a_1 \cdot r^3 = -1 \cdot 3^3 = -1 \cdot 27 = -27 \]

5. Fifth term:
   \[ a_5 = a_1 \cdot r^4 = -1 \cdot 3^4 = -1 \cdot 81 = -81 \]

So the first five terms of the geometric sequence are: \[ -1, -3, -9, -27, -81 \]