Question 1204372


 

{{{n}}}th term of G.P is 


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


Given that,

{{{a[2]=6}}}
{{{a[5]=48}}}
 

{{{a[2]=a[1]*r^(2-1)}}}
{{{6=a[1]*r}}}
{{{ a[1]=6/r}}}.....eq.1


{{{ a[5]=a[1]*r^(5-1)}}}
{{{48=a[1]*r^4}}}
 {{{a[1]=48/r^4}}}.....eq.2


from eq.1 and eq.2 we have

{{{6/r=48/r^4}}}
{{{6r^4=48r}}}....simplify
{{{r^3=8}}}
{{{r=2}}}


then

{{{a[1]=6/2}}}.....eq.1
{{{a[1]=3}}}


your {{{n}}}th term equation is

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

now find {{{10}}}th term


{{{a[10]=3*2^(10-1)}}}
{{{a[10]=1536}}}