The numbers of terms in the expansion of (a+b+c)n , where n∈N , is

(a+(b+c))n=an+nC1an−1(b+c)1+nC2an−2(b+c)2+....+nCn(b+c)n Further expanding each term of R.H.S.First term on expansion given one termSecond term on expansion gives two termsThird term on expansion gives three terms and so on.∴  Total no. of terms =1+2+3+....+(n+1)=(n+1)(n+2)2 Hence (A) is the correct answer.