Question 1179160


If the information given below represents a geometric sequence , find . {{{a[3]}}}?

{{{a[1]=3645}}}
{{{a[6]=15}}}

formula for nth term of a geometric sequence:

{{{a[n]=a[1]*r^(n-1)}}}

use given to find common ratio {{{r}}}

{{{15=3645*r^(6-1)}}}

{{{15/3645=r^5}}}

{{{r^5=1/243}}}

{{{r=root(5,1/243)}}}

{{{r=1/root(5,243)}}}

{{{r=1/root(5,3^5)}}}

{{{r=1/3}}}

{{{a[n]=3645*(1/3)^(n-1)}}}

then

{{{a[3]=3645*(1/3)^(3-1)}}}

{{{a[3]=3645*(1/3)^2}}}

{{{a[3]=405}}}