Enterbot3 Posted October 22, 2018 Report Share Posted October 22, 2018 A sequence {un} is defined by u0 = 1, u1 = 2, un+1 = 3un – 2un–1 – 1 where n ∈Z. (a) Find u2, u3 and u4. My book says that U2=4, U3=8 and U4=16. And that based on those numbers the formula for n is 2^n+1, which makes sense but what I dont get is how would you verify this formula to satisfy the equation (un+1 = 3un – 2un–1 – 1)? Reply Link to post Share on other sites More sharing options...
kw0573 Posted October 22, 2018 Report Share Posted October 22, 2018 I think there is an error with the problem, because u2 should be 3(2) - 2(1) - 1 = 3, but the answer given is 4. Even then, the general un is 2^n not 2 ^(n+1) or 2^n + 1 Reply Link to post Share on other sites More sharing options...
Guest Posted October 23, 2018 Report Share Posted October 23, 2018 The question is definitely wrong. un+1 =/= 3un - 2un -1 -1. That would just mean un+1=un-2? That's not possible in any case. Reply Link to post Share on other sites More sharing options...
Enterbot3 Posted October 23, 2018 Author Report Share Posted October 23, 2018 Yeh. I think that the book has made some errors. Reply Link to post Share on other sites More sharing options...
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