Sum of Look and Say Sequence
I'd have to ask - do you have to Console.WriteLine() the output? Most code testing sites want a return value from a method rather than looking at the console output and clearly, the console output is going to be the vast majority of the time spent in the application.

Secondly, I have a few quick and easy tips for increasing performance:


Ditch the string.Concats - you have the StringBuilder in hand and can just 
.Append() each of those items in turn:


stringBuilder.Append(count);
stringBuilder.Append(char.GetNumericValue(digit));


in the loop and

stringBuilder.Append(count);
stringBuilder.Append(digit);


after the loop.


Pre-allocate list size: List&lt;string&gt; sequence = new List&lt;string&gt;(nthTerm + 1) { "1" }; This will reduce reallocations as the list grows (it starts at 4 and then increases by twice the size as necessary).
Measure with precision - surround your processing code in Main with var SW = Stopwatch.StartNew(); and Console.WriteLine(sw.Elapsed);. This will show you the time your code actually took.


After I did these all the things listed above, 2 ran in 00:00:00.0006395 and 50 ran in 00:00:00.5806011.