Question
1 Identify the pattern for the following sequence. Find the next three terms in the sequence. I \( -1,3,-9,27 \), a. Multiply by \( 3 ; 81,243,729 \) b. Multiply by \( -3 ;-81,243,-729 \) c. Multiply by \( -3 ; 81,243,729 \) d. Multiply by \( 3 ;-81,-243,-729 \)
Ask by Patel Whittaker. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The next three terms are \(-81, 243, -729\).
Solution
To identify the pattern in the sequence \(-1, 3, -9, 27\) and determine the next three terms, let's analyze the progression:
1. **Identify the Pattern:**
- Starting with \(-1\):
- \(3 = (-1) \times (-3)\)
- \(-9 = 3 \times (-3)\)
- \(27 = (-9) \times (-3)\)
The pattern involves **multiplying by \(-3\)** each time.
2. **Determine the Next Three Terms:**
- \(27 \times (-3) = -81\)
- \(-81 \times (-3) = 243\)
- \(243 \times (-3) = -729\)
Therefore, the next three terms are \(-81, 243, -729\).
3. **Choose the Correct Option:**
- **Option b** states: "Multiply by \(-3\); \(-81, 243, -729\)", which matches our findings.
**Answer:**
**b. Multiply by \( -3 \); \(-81,243,-729 \)**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
The sequence \( -1, 3, -9, 27 \) alternates signs and is formed by multiplying each term by \( -3 \). Specifically, \( -1 \times -3 = 3 \), \( 3 \times -3 = -9 \), and \( -9 \times -3 = 27 \). Continuing this pattern, we find the next terms by multiplying \( 27 \) by \( -3 \) repeatedly. This leads us to \( 27 \times -3 = -81 \), \( -81 \times -3 = 243 \), and \( 243 \times -3 = -729 \). So the next three terms in the sequence are \( -81, 243, -729 \). The correct answer is b: Multiply by \( -3; -81, 243, -729 \).
