question archive A geometric sequence is always of the form ##t_n=t_"n-1"*r## Every next term is ##r## times as large as the one before
A geometric sequence is always of the form ##t_n=t_"n-1"*r## Every next term is ##r## times as large as the one before
Subject:MathPrice: Bought3
A geometric sequence is always of the form ##t_n=t_"n-1"*r##
Every next term is ##r## times as large as the one before.
So starting with ##t_0## (the "start term") we get: ##t_1=r*t_0## ##t_2=r*t_1=r*r*t_0=r^2*t_0## ...... ##t_n=r^n*t_0##
Answer: ##t_n=r^n*t_0## ##t_0## being the start term, ##r## being the ratio
Extra: If ##r>1## then the sequence is said to be increasing if ##r=1## then all numbers in the sequence are the same If ##r<1## then the sequence is said to be decreasing , and a total sum may be calculated for an infinite sequence: sum ##sum=t_0/(1-r)##
Example : The sequence ##1,1/2,1/4,1/8...## Here the ##t_0=1## and the ratio ##r=1/2## Total sum of this infinite sequence: ##sum=t_0/(1-r)=1/(1-1/2)=2##
