26. $$ +1,-5,+25,-125, ?, ?, ? $$

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UpStudy AI · Accepted Answer

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 $$ +625, -3125, +15625 $$.
The missing terms in the sequence are $$ +625, -3125, +15625 $$.

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