The remainder when Q=1+3+3^2+3^3+..........+3^200 is divided 13.  Choose the correct choice from the following options
A) 12  B) 7  C) 0  D) 5  E) 3
Q=1+3+3^2+3^3+..................+3^200   Is a Geometric progression having common ratio as '3' and number of terms as '201'.   Since Sum to n terms in GP = a(r^n-1)/(r-1)   where a=First term and r =common ration   Hence,   1*(3^201 -1 )/(3-1)   Rem of (3^201-1)/2 divided by 13   3^201 -1 /26   WKT, 3^3 = 27 = 26+1   {(26+1)^67 - 1}/26   {1-1}/26   =&gt;0.0
<result>C</result>
The remainder when Q=1+3+3^2+3^3+..........+3^200 is divided 13.