Question 773412
In a geometric sequence the ratio of consecutive terms equals a number {{{r}}}, called the common ratio.
The nth term of a geometric sequence is given by
{{{b[n]=b[1]*r^(n-1)}}} where
{{{b[1]}}} is the first term, and
{{{r}}} is the common ratio
The sum of the first n terms is {{{S[n]=b[1]*(r^n-1)/(r-1)}}}
 
In your case,
{{{b[1]=19}}}
{{{b[6]=19*r^(6-1)=19*r^5=319333}}}
 
{{{19*r^5=319333}}} --> {{{r^5=319333/19}}} --> {{{r^5=16087}}} --> {{{r=root(5,16087)}}} --> {{{r=7}}}
 
{{{S[6]=19*(7^6-1)/(7-1)}}} --> {{{S[6]=19*(117649-1)/6}}} --> {{{S[6]=19*117648/6}}} --> {{{highlight(S[6]=372552)}}}