# Look at these:1 × 4 = (2 × 3) – 22 × 5 = (3 × 4) – 23 × 6 = (4 × 5) – 24 × 7 = (5 × 6) – 2i) Write the next two lines in this pattern.ii) If we take four consecutive natural numbers, what is the relation between the products of the first and the last, and the product of the middle two?iii) Write this as a general principle in algebra and explain it.

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Algebric Identities46 mins
Discussion on Algebric Identities48 mins
Algebric Expressions and Identities45 mins
Algebraic Expressions and Identities43 mins
Master Algebraic Identities43 mins
Division of Algebraic Expressions36 mins
Smart Revision | Quiz on Algebraic Expression and Identities44 mins
How to Use Algebraic Identities40 mins
Multiplication of Algebraic Expression40 mins
Genius Quiz | Algebraic Expressions and Identities30 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses