how do i derive an explicit sequence from a recursive one, where a sub (n-1) appears more than once

[river fable]

Example:

[gusty surge]

you can do something like :
1/a_n = (1 + 3a_(n-1)) / a_(n-1)
= 3 + 1/a_(n-1)
so 1/a_n - 1/a_(n-1) = 3
1/a_(n-1) - 1/a_(n-2) = 3
1/a_(n-2) - 1/a_(n-3) = 3
...
1/a_1 - 1/a_0 = 3
---------------------------- +
1/a_n - 1/a_0 = 3n
1/a_n = 3n + 1/a_0

if u find a fractional recursive formula like this one, i suggest trying to do something like i did

[also nice username]

[marble siren]

I’ve never seen that before, I that’s fascinating

[river fable]

Turns out there was a very visible pattern.

[ripe cypress]

.solved