Question

I need help in finding the solution to the recurrence relation: a_n = a_n-1 - n; a_0 = 4.

i know the terms are: 4,3,1,-2,-6,-11 ... but im having trouble finding a closed form solution. Any help would be appreciated. (In the formula a_n means a with subscript n and likewise for the other terms.

Answer 1

can you find out the rule of the sequence 1, 3, 6, 10, 15.... ?

Answer 2

only just like +2,+3,+4,+5 but thats not in a solution form

Answer 3

I know, I can construct the solution for your problem, just forgot the rule of the sequence I give out above. If I have it, your solution is done.

Answer 4

ok, we can do together, I give you mine, and you finish your stuff.

Answer 5

you have \[a_n = a_{n-1} -n\] so
\[a_1= a_0 -1\\a_2 = a_1 -2=a_0-1-2=a_0-3\\a_3= a_2-3=a_0-3-3=a_0-6\\a_4=a_3-4=a_0-6-4=a_0-10\\a_5= a_4-5=a_0-10-5=a_0-15\] so, your recurrent sequence will have the terms like this, every term base on \(a_0\), the problem is finding out the rule of the "remote" numbers. then you are done. I took it last year, forgot how to do next

Answer 6

discrete math, right? after claiming the formula, have to use induction to prove what we claim, right?

Answer 7

yeah its discrete math. Thanks for the help. :) I appreciate it.

Answer 8

ok, good luck, I try all my best, but it's too late here, need sleep. Trust me, that the way to find out the closed form of the sequence.