1.

Observe the following operations1 × 4 = (2 × 3) – 2 2 × 5 = (3 × 4) – 2 3 × 6 = (4 × 5) – 2 4 × 7 = (5 × 6) – 2(i) Write next operations of two rows in the same order.(ii) Among the 4 nearest natural numbers. Find the relation- ship between the product of first and last and those in the middle.(iii) Write the principle in algebraic expression and explain the reason

Answer»

(i) 5 × 8 = (6 × 7) – 2

6 × 9 = (7 × 8) – 2

(ii) The product of first and last numbers = 2 subtracted from the product of two middle numbers.

(iii) The numbers are n, n + 1, n + 2, (n + 3) n (n + 3) = n2 + 3n

(n + 1) (n + 2) = n2 + 3n + 2

difference = 2



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