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 :
tn = 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 :
Sn = a (rn – 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