Study the pattern:
1 × 8 + 1 = 9 1234 × 8 + 4 = 9876
12 × 8 + 2 = 98 12345 × 8 + 5 = 98765
123 × 8 + 3 = 987
Write the next two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).
Solution:
The next two steps would be:
and
One of the way to understand this pattern is following:
Ist term
2nd term
Ist term
3rd term
= 888 + 88 + 8 + 2 + 1 = 888 + 2nd term + 1
Similarly, 4th term = 8888+ 3rd term + 1
5th term = 88888+ 4th term + 1
And so on..
(Distributivity of multiplication over addition plays an important role to make this pattern.)
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