1. **Problem 1:** Complete the sequence where each term is of the form $\text{number} \times 8 + \text{digit}$. 2. **Observation:** The pattern shows that multiplying the number formed by consecutive digits starting from 1 by 8 and then adding the last digit of that number results in a descending sequence of digits from 9 downwards. 3. **Formula:** For the $n$-digit number $N = 123\ldots n$, the expression is: $$N \times 8 + n = \text{a number with digits } 9, 8, 7, \ldots, (10-n)$$ 4. **Calculate missing values:** - $12345 \times 8 + 5 = 98765$ - $123456 \times 8 + 6 = 987654$ - $1234567 \times 8 + 7 = 9876543$ - $12345678 \times 8 + 8 = 98765432$ - $123456789 \times 8 + 9 = 987654321$ --- 5. **Problem 2:** Complete the sequence where each term is of the form $\text{number} \times 9 + \text{digit}$. 6. **Observation:** Multiplying the number formed by consecutive digits starting from 0 by 9 and adding an increasing digit results in a number consisting of repeated 1's. 7. **Formula:** For the $n$-digit number $M = 0,1,12,123,\ldots$, the expression is: $$M \times 9 + (n+1) = \underbrace{111\ldots1}_{n+1 \text{ times}}$$ 8. **Calculate missing values:** - $1234 \times 9 + 5 = 11111$ - $12345 \times 9 + 6 = 111111$ - $123456 \times 9 + 7 = 1111111$ - $1234567 \times 9 + 8 = 11111111$ - $12345678 \times 9 + 9 = 111111111$ **Final answers:** **Sequence 1:** 98765, 987654, 9876543, 98765432, 987654321 **Sequence 2:** 11111, 111111, 1111111, 11111111, 111111111