15n^(2)-28=n

The number of natural numbers n for which (15n^2+8n+6)/n is a natural number is:

If .^(n)C_(2)=28 , find n.

If n is a positive integer (gt1) , show that, (4^(2n+2)-15n-16) is always divisible by 225.

Find (i) the n^(th) term and (ii) the sum of first n terms of the series 6+15x+28x^(2)+45x^(3)+...

If n>1 be a +ve integer,then using binomial theorm show that (4^(2n+2)-15n-16) is always divisible by 225.