Question

d and b
3n-1 3n-3 3-5
+
13.
Find the indicated term for the series
n
n
Can we deduce 1s? If so what is its value, if not why?​

Answer 1

Answer:

If n is an integer greater than 6, which of the following must be divisible by 3 ?

(A) n(n + 1)(n – 4)

(B) n(n + 2)(n – 1)

(C) n(n + 3)(n – 5)

(D) n(n + 4)(n – 2)

(E) n(n + 5)(n – 6)

Since 3 is a prime number then in order the product to be divisible by 3 either of the multiples must be divisible by 3. Now, to guarantee that at least one multiple is divisible by 3, these numbers must have different remainders upon division by 3, meaning that one of them should have the remainder of 1, another the reminder of 2 and the third one the remainder of 0, so be divisible by 3.

For option A: n and n+1 have different remainder upon division by 3. As for n-4, it will have the same remainder as (n-4)+3=n-1, so also different than the remainders of the previous two number.