does this recurrance relation make sense ?

Question

write the first 4 terms when

Un+2=Un+1 + Un , where,u1=1 and U2=1

I got the impression that U2 would have to be more than 1 as un+1+un=u2 (is that right), if it is then u2= more than 1 ??????
As you can see im trying too hard and should be out there drinking alchohol. If you can, then please answer, (its going to a good cause). Thanks and happy new year

Answer 1

U3 = U2 + U1 = 1 + 1 = 2
U4 = U3 + U2 = 2 +1 = 3 etc
No it is fine for U2 = 1

Answer 2

u1=1
u2=1
u3=1+1=2
u4=1+2=3

Answer 3

sure, your recurrence relation says that any term in the sequence is the sum of the two prior terms in the sequence, or, the (n+2)nd term is the sum of the (n+1)st term and the nth term.

As someone has noted, this is how the Fibonacci sequence works.

the first two terms in the Fibonacci sequence are defined as 1, 1, so the next terms are 2,3, 5, 8, 13, 21, 34, 55...note that each term is the sum of the two prior terms

Answer 4

You just described the classic Fibonacci Sequence.

There's a ton of material on it online, as well as whole books about it.