posted by Kate .
The sequence < un > is defined by the recurrence
Un+1 = 3Un+1\5Un+3
initial condition of u1 = 1:
Need to show un in terms of Fibonacci / Lucas numbers
I assume you mean
Un+1 = 3Un + 1/(5Un+3)
since no other interpretation makes any sense.
But that's not an integer sequence. So, how about fixing your typos, using parentheses, and maybe say U<n+1> to avoid mixing subscripts with numeric values?