Question
Point)Suppose the first four terms of the sequence {an } is given:4,0114,42 44,d3 134_Find linear recurrence of the form=S @n-1 + [that correctly describes the pattern of the terms above: Enter the correct values for and in the answer boxes below:Note: You can earn partial credit on this problem:
point) Suppose the first four terms of the sequence {an } is given: 4,01 14,42 44,d3 134_ Find linear recurrence of the form =S @n-1 + [ that correctly describes the pattern of the terms above: Enter the correct values for and in the answer boxes below: Note: You can earn partial credit on this problem:
Answers
Recurrence relations Write the first four terms of the sequence $\left {a_{n}\right\}$ defined by the following recurrence relations. $$a_{n+1}=2 a_{n}: a_{1}=2$$
Even recurrence relations. When we have that, I am this one equal to 1/1 plus and and then we have the Isiro. Commit to one. Let's try to find one you could you want on the one plus one. And now include your half a Jericho Julian over one plus 1/2. You go to 1/3 out of two and equal to two out of three. Adrian, could you 1/1 plus jointed tree in Could you won over hair head of 503 and they could you three under five, a far echo to one on one. Find a threat of five here. And then we get equal Jew you're gonna need out of five and then begin the 5 to 8.
For this problem we've been given the first here years were asked to find the next four. Main thing that we need to do is find our diesel. How do I move from one to the neck? And that is by minus four. We know because they told us Here, let's start. Remember, we do age the n minus one plus R D term during 5.9 minus 2.4. All right, 5.5, mind four. Five point 5.1 minus point for me. Four point 4.7 minus point for four point and we're done.
Hello? So here we have the sequence negative 1/4 and then two nights and the negative 3/16 and then four 25th and the negative 5 36 and so on. So we see here that the numerator is just for the counting numbers. But we alternate uh when we start negative negative positive negative positive negative positive right? But we're gonna be discounting 12345 and so on. And the denominators are going to be um While powers here right the denominator is just the form basically um N plus one to the end. So a formula here could be what we want negative we want um basically just end times negative one to the end and give us a numerator. And then the denominator is just going to be but we were starting at um and is equal to two. We're starting at two squared. So therefore the denominator here is going to be a n plus one squared.
No doubt for all these terms, there is a one, and for the first term It's one or 2. For a second term, it's one or three and then one or four in one world, five has a because one plus one over and plus one.