Question 697063

Substitute {{{21}}} for {{{a2}}} and {{{567}}} for {{{a5}}} in the formula


{{{an = a1* r^(n-1)}}}


{{{a2= a1* r^(2-1)}}}...-> ..{{{a1*r=21}}}


{{{a5= a1* r^(5-1)}}}...->..{{{ a1*r^4=567}}}


Substitute this expression for a1 in the second equation and solve for r.


 {{{a1 =21/r}}}


{{{a1*r^4=567}}}


{{{(21/r)*r^4=567}}}


{{{21*r^3=567}}}


{{{r^3=567/21}}}


{{{r^3=27}}}


{{{r=3}}}


Substitute for {{{r}}} in the first equation and solve for {{{a1}}}.


{{{a1* r=21}}}


{{{a1*3=21}}}


{{{a1 =21/3}}}


{{{a1 =7}}}


Now use the formula to find the nth term {{{an}}}.


{{{highlight(an= 7*3^(n-1))}}}