# Computing a recurrence table backward

I am trying to understand how to compute a recursive equation backward say n = 10 to n = 1. I am trying to solve a PDE for which the solution is only known in at some future time and that future value can be used to find a value at an earlier time. Can you please help me understand how I can get following series of multiples of 7 starting from 10th element which is 7. I tried the following code, but it did not work.

RecurrenceTable[a[n - 1] == 3 a[n], a == 7, a, {n, 10, 1, -1}]

• You could do a forward recurrence with a==x and then solve for x at the end. – b.gates.you.know.what May 2 '15 at 9:13
• did you suggest RecurrenceTable[{a[n + 1] == 3 a[n], a == x, a == 7}, {a, x}, {n, 1, 10}]. I get a error "RecurrenceTable::underdet: There are more dependent variables than equations, so the system is underdetermined" – Kausik May 2 '15 at 9:24
• Try aux = RecurrenceTable[{a[n - 1] == 3 a[n], a == x}, a, {n, 1, 10}]; aux /. Solve[Last[aux] == 7, x]. – b.gates.you.know.what May 2 '15 at 11:31
• Many thanks for that. I will use it solve FDE – Kausik May 2 '15 at 11:38

b.gatessucks solution given in a comment should be recorded answer.

aux = RecurrenceTable[{a[n - 1] == 3 a[n], a == x}, a, {n, 10}]

{x, x/3, x/9, x/27, x/81, x/243, x/729, x/2187, x/6561, x/19683}

First[aux /. Solve[Last[aux] == 7, x]]

{137781, 45927, 15309, 5103, 1701, 567, 189, 63, 21, 7}


But, of course, in this simple case there is

Reverse @ NestList[3 # &, 7, 9]