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i) 5× 8 = (6× 7) – 2

6× 9 = (7× 8) – 2

ii) The above pattern is based on this statement only.

Let the four consecutive numbers be 1,2,3,4.

Product of first and last = (1× 4) = 4

Product of middle two terms = (2× 3) = 6

and 4 = 6 - 2

Let the four consecutive numbers be 4,5,6,7.

Product of first and last = (4× 7) = 28

Product of middle two terms = (5× 6) = 30

And 28 = 30 - 2

iii) General principle,

Let the four consecutive natural numbers be x , (x+1) , (x+2) , (x+3).

Product of first and last = x(x+3) = x² + 3x

Product of middle two terms = (x+1)(x+2) = x(x+2) + 1(x+2)

= x² + 2x + x + 2

= x² + 3x + 2

Clearly, we can see that the difference between the product of middle two terms and the product of first and last term is equal to 2.