26. \( +1,-5,+25,-125, ?, ?, ? \)

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 \( +625, -3125, +15625 \).