> So i had an online assessment for a job, it didnt go well. I cant work out one of the questions, which i think is fairly simple, but its annoying me. This is what I remember of the question.
> Bar graph showing that at 5 years 2.1 million, 10 years 3.5 million. Will 15 years be over 5 million. I think that was it.
If you've only got two data points, you can't say anything valid about a third point unless you make assumptions.
> (In reply to itsThere) Reminds me of a question I was asked once. What comes next in this sequence,
> 1, ....
> There is a pretty convincing answer which probably isn't what you first think of.
All sequence questions are normally answered with the simplest (lowest power) function which satisfies the initial conditions. In the case of 4, 8, 12 you can use the linear function 4n to fit the bill, but there are an infinite number of higher power solutions which have the same initial 3 terms. In the case of 1, 2, ... most people would say that the next term is 3 again ignoring the infinite higher power solutions such as f(n) = 2^(n-1)
Following this train of logic the lowest power function which fits 1, ... is f(n) = 1, so the sequence is 1, 1, 1, 1,
Quite strictly you shouldn't attempt to extrapolate beyond the range of your data as the relationship you observe may change beyond the boundaries.
As you might have noticed everyone who's providing an answer is using a conditional clause "if the relationship is linear". In many growth curves (e.g. population) growth is non-linear (e.g. exponential) and with only two prior observations you have no way of gauging this.
> (In reply to ablackett)
> >All sequence questions are normally answered with the simplest (lowest power) function which satisfies the initial conditions.
> Why would you do that? Seems rather arbitrary to me unless some extra context is given.
Occams Razor/maximum parsimony/KISS (Keep It Simple Stupid)
In reply to slacky: That's the kind of context I was referring to. Makes perfect sense from an applied perspective but no reason to make that sort of assumption in a purely mathematical context, which to me is what the question implies.
Guess im just being fidgety because my sense of mathematical decency has been ruffled!