Q. 53.9( 30 Votes )

Study the pattern

Answer :

From the given pattern, the 1st step is:  1× 8 + 1 = 9

And the 2nd step: 12 × 8 + 2 = 98, which can be written as :

(11 + 1) × 8 + 2

On following distributive property, we get,

= (11 × 8) + (1 × 8) + 2

= 88 + 8 + 2 = 98

Therefore, we can write the 3rd step: 123 × 8 + 3 = 987 as,

= (111 + 11 + 1) × 8 + 3

= 111 × 8 + 11 × 8 + 1 × 8 + 2

= 888 + 88 + 8 + 3 = 987

Similarly, 4th step:  1234 × 8 + 4 = 9876 as, 

= (1111 + 111 + 11 + 1) × 8 + 4

= 1111 × 8 + 111 × 8 + 11× 8 + 1 × 8 + 4

= 8888 + 888 + 88 + 8 + 4 = 9876

In the same way, the next steps are:

5th step: 12345 × 8 + 5, can be written as,

=  (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 = 98765

Thus, the 5th term is : 12345 × 8 + 5 = 98765

Now, the 6th step:  123456 × 8 + 6 can be written as,

= (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

Thus, the 6th step is: 123456 × 8 + 6  = 9876543 

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