Question

Study the pattern: 1 x 8 + 1 = 9; 12 x 8 + 2 = 98; 123 x 8 + 3 = 987

Answer 1

1234*8+4=9876. ............ would be the next series

Answer 2

1 × 8 + 1 = 9
12 × 8 + 2 = 98
i.e. (11 + 1) × 8 + 2 = 11 × 8 + 1 × 8 + 2 = 88 + 8 + 2 = 98
123 × 8 + 3 = 987 ;
i.e. (111 + 11 + 1) × 8 + 3 = 111 × 8 + 11 × 8 + 1 × 8 + 2
= 888 + 88 + 8 + 3 = 987
1234 × 8 + 4 = 9876 ;
i.e. (1111 + 111 + 11 + 1) × 8 + 4 = 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 4
= 8888 + 888 + 88 + 8 + 4 = 9876
12345 × 8 + 5 = 98765
i.e. (11111 + 1111 + 111 + 11 + 1) × 8 + 5
= 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 5
= 88888 + 8888 + 888 + 88 + 8 + 5 = 98765
Extending the pattern, we have
123456 × 8 + 6
= (111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + 5
= 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 5
= 888888 + 88888 + 8888 + 888 + 88 + 8 + 6 = 987654
1234567 × 8 + 7
= (1111111 + 111111 + 11111 + 1111 + 111 + 11 + 1) × 8 + 7
= 1111111 × 8 + 111111 × 8 + 11111 × 8 + 1111 × 8 + 111 × 8 + 11 × 8 + 1 × 8 + 7
= 8888888 + 888888 + 88888 + 8888 + 888 + 88 + 8 + 7 = 9876543