Can you explain to me the Method Of Differences in Sequence and Series?

Lets take an example for better understanding. For arithmetic progression 3+7+13+21+......We can clearly see that the 1st difference is in AP4+6+8+....If 1st different is in ap then we can write Tn=an^2+bn+cBy putting values of n u can make 3 equations and find a, b, cFor this case a=b=c=1Tn=n^2+n+1Then summation of Tn=(n(n+1)(n+2))/3 + nSimilarly if 2nd difference is in ap thenTn=an^3+bn^2+cn+d and so on. If 1st term is in GP then Tn=@R^(n-1)+a and prosegure will remain same.