Question

(i) Take any three consecutive odd numbers and find their product; for example, $1\times 3\times 5=15,3\times 5\times 7=105,5\times 7\times 9-......$
(ii) Take any three consecutive even numbers and add them, say, $2+4+6=12,4+6+8=18,6+8+10=24,8+10+12=30$ and so on.
Is there any pattern you can guess in these sums? What can you conjecture about them?

Answer 1

(i)The possible three conjucture are:
a) The product of any three consecutive odd number is odd.
b) The product of any three consecutive odd number is divisible by $3$.
c) The sum of all the digits present in product of three consecutive odd numbers is even.
(ii) The possible three conjuctures are:
a) The sum of any three consecutive number is always even.
b) The sum of any three consecutive number is always divided by $3$.
c) The sum of any three consecutive number is always divided by $6$.