Question 175216
The first two terms of a geometric sequence are {{{a[1]=1/3}}} and {{{a[2]=1/6}}}. How do I find {{{a[8]}}}, the eighth term?
<pre><font size = 4 color = "indigo"><b>
First find the common ratio, {{{r}}}, by dividing any term by
its preceding term.  So 

{{{matrix(1,17, r, "=", a[2]/a[1], "=", (1/6)/(1/3), "=", 1/6, "÷", 1/3, "=", 1/6, "×", 3/1, "=", 3/6, "=", 1/2))}}}

Now use the formula for the {{{n}}}th term:

{{{matrix(1,4,a[n], "=", a[1],r^(n-1))}}} 

Substitute {{{n=8}}}

{{{matrix(1,3,a[8], "=", a[1]r^(8-1))}}}

{{{matrix(1,3,a[8], "=", a[1]r^7)}}}

{{{matrix(1,3,a[8], "=", (1/3)(1/2)^7)}}}

{{{matrix(1,3,a[8], "=", (1/3)((1^7)/(2^7)))}}}
            
{{{matrix(1,3,a[8], "=", (1/3)(1/128))}}}

{{{matrix(1,3,a[8], "=", 1/384)}}}

Edwin</pre>