Advice on Learning Series/Sequences

Hello!

Currently I’m at the tail end of the Algebra modules, but I’m just stuck on trying to wrap my head around Sequences and Series. The last question in the Sequence 1 exercise I still do not understand even after it’s being explained. I get the basic “list” and “sum” part, but when it comes to rules and understanding notation I’m completely lost. Any advice or help to better understand them?

Can you please share the question as reference to help explain better.

This one in particular I’m struggling to understand.

The explanation “Notice that the first equation of an is defined only in terms of n this means that” all = 3.Apparently, it’s just an approximation of three?

And then Series in general I’m concerned about because of the need to have a sort of intuition to get them.

These two in particular I’m hung up about.

To be very honest, such type of questions wouldn’t come for the GRE.
They are pretty hard.

For the first one, for every term, only the root5 term would remain for every term inside (as the rest would get cancelled out, due to the alternate + and -), and this root5 term would get cancelled by the root5 in the denominator, hence you get integer values for every term.

For the second and the third, there is a direct formula, for the sum of a Geometric Sequence (again not expected to know for the GRE)
The formula is:
a x (r^n - 1)/r - 1

I hope this makes things a bit clearer.

The point is that Q2 guides students on deriving the formula, and Q3 is an application of that.

Yeah true.

But I haven’t really heard that a question on Sum of a Geometric Progression be asked in the GRE.

But of course, always good to know.

Try putting n = 3 in that equation and see what you get.