The sum of n  terms of two arithmetic series are in the ratio 2n+3  :6n+5 , then the ratio of their 13th  terms is

Given that the sum of n terms of two arithmetic series is in the ratio 2n+3  :  6n+5 ⇒              (Sn)1(Sn)2=2n+36n+5      .......(i) Where Sn  is the sum of n  terms of an arithmetic series. We know that,Sn=n2[2a+(n−1)d] From Equation (i), we get  (Sn)1(Sn)2=n2[2a1+(n−1)d1]n2[2a2+(n−1)d2]=2n+36n+5 ⇒    2a1+(n−1)d12a2+(n−1)d2=2n+36n+5 For a=13⇒n=2a−1=2×13−1=25 ∴                   2a1+(25−1)d12a2+(25−1)d2=53155 ⇒                  a1+12d1a2+12d2=53155 ⇒                      (T13)1(T13)2=53155