prove that Sn - Sn-1=an for geometry progression class 11th Math

LHS=

 Sn - S(n-1)

=a(1-r^n)/(1-r) - a(1-r^(n-1))/(1-r) 

=a((1-r^n)/(1-r) -(1-r^(n-1))/(1-r))

=a((1-r^n)-(1-r^(n-1)/(1-r))

=a((1-r^n)-(1-r^(n×r^1)/(1-r))

=a(1-r^n-1+ r^(n)×r^-1)/(1-r))

= a(1-r^n- 1+ r^(n)×r^-1)/(1-r))

= a(-r^n- + r^(n)×1/r)/(1-r))

= a(r^(n)×r-r^n )/(1-r))

= ar^n(1/r-1)/(1-r))

=ar^n(1-r)/r(1-r))

=ar^n/r

=ar^(n-)