Question

Take any consecutive odd numbers and find the product as follows
1$\times$3$\times$5 = 15, 3$\times$5$\times$7 = 105 ..
5$\times$7$\times$9 = 315....... Find the conjecture for this pattern.

• A. (n-1)$\times$n$\times$(n+2)
• B. n$\times$(n+2)$\times$(n+3)
• C. $n^3$ - $4n$
• D. $n^3$ - $4$

Answer 1

The correct option is C $n^3$ - $4n$

Let middle term be n hence predecesor term will be (y-2) and successor team will be (y+2)
hence according to pattern
= (y-2)$\times$y$\times$(y+2)
= y$\times$(y+2)$\times$(y-2) = y$\times$($y^2$ - 4)
= $y^3$ - $4y$
= $n^3$ - $4n$
like for n=3
1$\times$3$\times$5 = $3^3$ - 4$\times$3 = 27 - 12 = 15