series

[Kombmail]

http://www.projectmaths.com.au/assets/M-2014-8.pdf
this answer i get what formula to use but i dont get how it is 11?

[RuiAce]

You should look at what the answers have and then try multiple values of \(n\) that make sense.

The first term has \(x^1\) appearing, as does the common ratio. So the second term should have \(x^2\) appearing; the third term should have \(x^3\) appearing, and so on forth. So in general, we expect that the \(n\)-th term has \(x^n\) appearing.

Since our multiple choice options involve \(x^{10}\) and \(x^{11}\), the only plausible options are \(n=10\) and \(n=11\). At this point, we only have guess and check to rely on (that is, unless you're willing to spend time computing every term in the sequence). If we try subbing \(n=10\) first, we'll realise that it doesn't work, so we have to sub \(n=11\) anyway.