[?] Solve a recurrence relation?

Questions
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1

I have been having trouble doing reccurence relation problems in my discrete structures class, this is one question I have been struggling on:

Solve the reccurence relation a_n = 3a_(n-1)+10a_(n-2) with initial terms a_0 = 4 and a_1 = 1

I need some work to be shown so I can better understand the process! Thanks!

2

In[3]:= RSolve[(a[n] == 3 a[n - 1] + 10 a[n - 2]), a[n], n]

Out[3]= {{a[n] -> (-2)^n C[1] + 5^n C[2]}}

Mathematica has (as far as I know) the best solver (available) for Recurrence Relations.

Without having done any work or thinking on my part: it seems you can use the answer to chooser your two Constants by the rule given. (or do more work to set constants, as the next person did)

3

RSolve[{a[n] == 3 a[n - 1] + 10 a[n - 2], a[0] == 4, a1 == 1}, a[n], n]

 (*  {{a[n] -> 1/7 (19 (-2)^n + 9 5^n)}}  *)

For more info see here.