a) Terms of quadratic sequence is of the form an^2 + bn +c
when n=1, i.e the first term = a+b+c =4 (given). ------------------(1)
And the first difference is 3a+b = 6 (given) -----------------------(2)
and the second difference is 2a = 2 (given)
So a=1
Putting the value of a in eq(2) we get:
b=3
Putting the value of b in eq(1) we get:
c=0
So the general term, Tn = 1n^2 + 3n + 0 = n^2 +3n
b)
T1 = 4 (given)
T2 = 2^2 + 3*2 = 10
T3 = 3^2 + 3*3 = 18
c) T100 = 100^2 + 3*100 = 10000+300 = 10300