Question 1197284



 general term is:

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


given:

3rd term is {{{a[3]=432}}}
5th term is {{{a[5]=15552}}}



find  {{{a[1]}}} and {{{r}}}


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

{{{432= a [1]* r^2}}}...........solve for {{{a[1]}}}

{{{a [1]=432/r^2}}}..............eq.1



{{{15552= a [1]* r^( 5 -1)}}}

{{{15552= a [1]* r^4}}}...........solve for {{{a[1]}}}

{{{a [1]=15552/r^4}}}..............eq.2



from eq.1 and eq.2 we have


{{{432/r^2=15552/r^4}}}........cross multiply

{{{432r^4=15552r^2}}}..........simplify

{{{432r^2=15552}}}

{{{r^2=15552/432}}}

{{{r^2=36}}}

{{{r=6}}}


go to


{{{a [1]=432/r^2}}}..............eq.1, substitute {{{r}}}

{{{a [1]=432/6^2}}}

{{{a [1]=432/36}}}

{{{a [1]=12}}}


your nth term formula is:


 {{{a[ n]= 12* 6^( n -1)}}}


then, the 12th term will be


 {{{a[ 12]= 12* 6^( 12 -1)}}}


 {{{a[ 12]= 12* 6^11}}}


{{{a[ 12]= 4353564672}}}