A sequence of number u1,u2,u3.. satisfies the relation (3n-2) Un +1 =(3n+1) Un, for all positive intergers n, if U1=1.find Un+1=U3 and u4

Answer 1

To find U3, we substitute n=1 into the given relation:

(3(1)-2) U2 + 1 = (3(1)+1) U1
U2 = 2U1 = 2(1) = 2

Then, substituting n=2 into the given relation, we can find U3:

(3(2)-2) U3 + 1 = (3(2)+1) U2
4U3 + 1 = 7(2)
4U3 = 13
U3 = 13/4

To find U4, we substitute n=3 into the given relation:

(3(3)-2) U4 + 1 = (3(3)+1) U3
7U4 + 1 = 10(13/4)
7U4 = 123/4
U4 = 123/28

Therefore, U3 = 13/4 and U4 = 123/28.