What are the effects of technological advancement on the financial and economic growth of a nation?

In the long run, technology is the primary determinant of economic growth -- if not the only one.

That's a pretty strong statement, so let me explain: In the short run, all sorts of things can affect a nation's economic growth, ranging from geopolitical shocks (like the OPEC oil crisis in the 1970s) to wars (pick your favorite) to various social and economic policies (tax rates, social insurance, empowerment of women).

Many of these things can also affect the total output of a country -- empowerment of women effectively doubles your labor force, and, sure enough, it really does seem to double your standard of living (possibly more than double, by positive feedback loops and the effect of specialization). Indeed, every time a country has grown from Third World to First World status, that country had substantial gains in the empowerment of women.

Social policies and tax rates are not, however, the reason why we live in a world with smartphones and airplanes instead of a world with smoke signals and horses. That's technology.

Technology is responsible for pretty much everything we think of as "the modern world," from factories to antibiotics, polyester to automobiles. Some things are really more a matter of infrastructure (Rome in 100 BC had sewer pipes and paved roads, but parts of India still don't today), but by far the largest determinant of our modern standard of living is technology.

Without technological advancement, you can produce goods, but only to a point; eventually products will wear out faster than they can be replaced. With technological advancement, you can become better at making stuff, and thus produce more and more every year. This is, in a nutshell, the Solow-Swan model; I just said it in words instead of equations.

Because technology has this permanent, sustainable effect, it is the primary determinant of economic growth in the long run -- so much so that it may as well be the only determinant. No social policy could have made Germany as rich in the medieval period as it is today. Despite all their infrastructure, Rome in 100 BC was still far poorer than Rome in 2015 AD. Technology is what made that difference.

Eventually we'll hit some kind of ceiling, because exponential growth can't go on forever. Despite Malthusian protestations to the contrary, though, we probably won't actually hit such a ceiling until we're all millionaires and colonizing other planets -- the Star Trek future, basically. Currently, technological advancement contributes about 1-2% GDP growth per year, and as far as we can tell should continue to do so through the rest of the 21st century. The most optimistic forecasts say it will get much faster, the most pessimistic say that it will stop; but the most probable forecasts suggest a very gradual slowing down.