For the second one, let be the limiting value, hence the recursive definition will give you:
Solve for .
Evening all, two questions here, first off I'm just sceptical with my answer for the first question, in great need of a second opinion in terms of my methods etc. The second question I'm really struggling where to start. Help would be much appreciated!
Firstly: The sum of the first four terms of an arithmetic sequence is 139 and the sum of the next four terms is 115. Find a and d:
[A] 4/2(2a + 3d) = 139
4a + 6d = 139
[B] 8/2(2a + 7d) = 115
8a + 28d = 115
Solving simultaneously: 16d = -163
d = -163/16
Substituting into equation [A]: 4a + 6(-163/16)=139
a = 1601/32
Second problem:
Given that, Un+1 = 3 - 1/3Un and U1 = 3
a) Find the values for U2, U3 and U4
b) Find the limiting value of Un as n tends to infinity.