Question 979019
In a Geometric Sequence each term is found by multiplying the previous term by a constant.

In general we write a Geometric Sequence like this:

{ {{{a}}}, {{{ar}}}, {{{ar^2}}}, {{{ar^3}}}, ... }

where:

    {{{a}}} is the first term, and
    {{{r}}} is the factor between the terms (called the "common ratio")

so, if first term is {{{a=2}}} and second term is {{{ar=1}}},  a constant (the "common ratio") is  {{{r=1/2}}}

and your sequence looks like this:
{ {{{2}}}, {{{1}}}, {{{2*(1/2)^2}}}, {{{2*(1/2)^3}}}, {{{2*(1/2)^4}}},{{{2*(1/2)^5}}},{{{2*(1/2)^6}}}... }

so, we can find out which term is {{{1/16}}} using the rule

to calculate any term:

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

(We use "n-1" because {{{ar^0}}} is for the 1st term)

{{{a[n] = 1/16}}}
{{{ar^(n-1)=1/16}}}

{{{2*(1/2)^(n-1)=1/16}}}

{{{(1/2)^(n-1)=1/32}}}

{{{(1/2)^(n-1)=1/2^5}}}

{{{(1/2)^(n-1)=(1/2)^5}}}

{{{n-1=5}}}

{{{n=5+1}}}

=> {{{n=6}}}......so, it is {{{6th}}} term

check:

{ {{{2}}}, {{{1}}}, {{{2(1/4)}}}, {{{2*(1/8)}}}, {{{2*(1/16)}}},{{{2*(1/32)}}},{{{2*(1/64)}}},... }

{ {{{2}}}, {{{1}}}, {{{1/2}}}, {{{1/4}}}, {{{1/8}}},{{{highlight(1/16)}}},{{{1/32}}},... }