Question 930752

{{{-3}}},{{{3/4}}},{{{-3/16}}},{{{3/64}}}...=>you are given a geometric sequence

so, the first term {{{a[1]}}} and the common ratio {{{r}}}, the nth (or general) term is given by:

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


use two terms to find the common ratio {{{r}}}:

1st {{{a[1]=-3}}} 

{{{r=a[2]/a[1]=(3/4)/-3=-3/12=-1/4}}}

check the formula:

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

{{{a[1] = -3*(-1/4)^(1-1)}}}

{{{a[1] = -3*(-1/4)^0}}}........{{{(-1/4)^0=1}}}

{{{a[1] = -3*1}}}

{{{a[1] = -3}}}


{{{a[2] = a[1]*r^(n-1)}}} if {{{n=2}}}

{{{a[2] = -3*(-1/4)^(2-1)}}}

{{{a[2] = -3*(-1/4)^1}}}........{{{(-1/4)^0=1}}}

{{{a[2] = -3*(-1/4)}}}

{{{a[2] = -3/-4}}}

{{{a[2] = 3/4}}}

this way you can find the terms coming after