help:find the big o notation

[jb123]

Let T(n) be defined by T(1) = 7 and T(n+1) = 3n+T(n) for all integers n>=1 . Which of the following
represents the order of growth of T( n) as a function of n ?
(A) Q(n)
(B) Q(n log n )
(C) Q(n^2)
(D) Q(n^2 log n)
(E) Q (2^n)


my answer is coming to be o(n^2)

plz if u can slove it

[f2003800]

T(n+1)=T(n)+3n
= T(n-1)+3(n+(n-1))
=T(n-2)+3(n+(n-1)+(n-2))

=T(n-(n-1))+3(n+(n-1)+(n-2).....+2+1)
=7+3(sum of first n numbers)
=7+3(n(n+1)/2)
which is O(n^2)

you are correct. no doubt in that.

[jb123]

oh yeah, i too did the same way