Question

Every even positive integer is of the form (a) ___ and every positive odd integer is of the form (b) ___.
(x is any positive integer)

• A. $a=2x^3,b=2x+2$
• B. $a=2x^2,b=2x+1$
• C. $a=2x,b=2x+1$
• D. $a=x,b=3x+1$

Answer 1

The correct option is C $a=2x,b=2x+1$

Every even positive integer is of form 2x
Let’s equate 2x for different values of ‘x’
x=1,2,3,4,5,6…
2x=2,4,6,8,10,12…….
From this we understand that 2x can be said as the general form for every even positive integer.

Every odd positive integer is of form 2x+1
Let’s equate 2x+1 for different values of ‘x’
x=0,1,2,3,4,5,6…
2x+1=1,3,5,7,9,11,13…….
From this we understand that 2x+1 can be said as the general form for every odd positive integer.