Question

Write the first five terms of the geometric sequence whose first term is negative 1​, and whose common ratio is 3.
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Part 1
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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:
\[
-1, -3, -9, -27, -81
\]