Pregunta
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The missing terms in the sequence are \( +625, -3125, +15625 \).
Solución
To solve the sequence \( +1, -5, +25, -125, ?, ?, ? \), let's analyze the pattern.
1. **Identify the pattern:**
- The first term is \( +1 \).
- The second term is \( -5 \).
- The third term is \( +25 \).
- The fourth term is \( -125 \).
2. **Observe the signs:**
- The signs alternate: \( +, -, +, - \).
3. **Observe the absolute values:**
- The absolute values are \( 1, 5, 25, 125 \).
- These can be expressed as powers of \( 5 \):
- \( 1 = 5^0 \)
- \( 5 = 5^1 \)
- \( 25 = 5^2 \)
- \( 125 = 5^3 \)
4. **Continuing the pattern:**
- The next absolute value should be \( 5^4 = 625 \).
- Since the last term was negative, the next term will be positive: \( +625 \).
5. **Next term:**
- Following \( +625 \), the next absolute value will be \( 5^5 = 3125 \), and since the previous term was positive, this term will be negative: \( -3125 \).
6. **Final term:**
- The next absolute value will be \( 5^6 = 15625 \), and since the previous term was negative, this term will be positive: \( +15625 \).
Thus, the complete sequence is:
\[
+1, -5, +25, -125, +625, -3125, +15625
\]
The missing terms are \( +625, -3125, +15625 \).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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The Deep Dive
This sequence follows a pattern where each term is multiplied by -5 to get to the next term. Starting from +1, we have: 1. \(1 \times -5 = -5\) 2. \(-5 \times -5 = +25\) 3. \(25 \times -5 = -125\) 4. \(-125 \times -5 = +625\) (next term) 5. \(625 \times -5 = -3125\) (next term) 6. \(-3125 \times -5 = +15625\) (next term) So, the next three terms in the sequence are \(+625, -3125, +15625\).

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