For week two of pre-calculus 11, we took similar concepts as in week one and applied them to geometric sequences. Geometric sequences are sequences which have a multiplying common ratio, rather than a common difference. We learned how to find a certain term in a sequence when each term is multiplied by a certain ratio, and how to find the sum of all the terms.

For example – to find a certain term in a geometric sequence, we use the formula :

t_{n }= a (r)^{n – 1 } meaning you multiply the first term (a) by the ratio to the power of one less than your term.

Or to find the sum of a geometric series :

S_{n} = a (r^{n} – 1)/r – 1 to find the sum of all your terms

Another thing we learned was that it is, in fact, possible to find the sum of all the terms in a never-ending infinite converging series.

The formula can be used if -1<r<1 :

S_{∞} = a/1 – r