Question 1126559



recall: In a Geometric Sequence each term is found by multiplying the previous term by a constant (common ratio {{{r}}}).

We can also calculate any term using the Rule:

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

If {{{8}}},{{{x}}},{{{y}}}, {{{27}}}, we know that

{{{a[1]=8}}}
{{{a[2]=x}}}
{{{a[3]=y}}}
{{{a[4]=27}}}

use first and fourth term, plug it in {{{a[n ]= a[1]*r^(n-1)}}} to find common ratio {{{r}}}

{{{27= 8*r^(4-1)}}}

{{{27/8=r^3}}}

{{{r^3=27/8}}}

{{{r^3=(3/2)^3}}}

{{{r=3/2}}}

now find second term: 

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

{{{a[2]= 8*(3/2)^(2-1)}}}

{{{a[2]= 8*(3/2)}}}

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

{{{a[2]= 12}}} ->{{{ x=12}}}


now find third term: 

{{{a[n ]= a[1]*r^(n-1)}}}...{{{n=3}}}


{{{a[3]= 8*(3/2)^(3-1)}}}}}}

{{{a[3]= 8*(3/2)^2}}}

{{{a[3]= 8*(9/4)}}}

{{{a[3]= 2*9}}}

{{{a[3]= 18}}} ->{{{y=18}}}


double check the fourth term:

{{{a[4]= 8*(3/2)^(4-1)}}}

{{{a[4]= 8*(3/2)^3}}}

{{{a[4]= 8*(27/8)}}}

{{{a[4]= 27}}} -> as given


so, the value of {{{x=12}}} and {{{y=18}}}