Answer Posted / narayanan

Let the 2 series have the sum S(1,n) and S(2,n).
now, S(1,n):S(2,n) = (5n+4):(9n+6)
= {5(n-1)+5+4}:{9(n-1)+9+6}
= {2*(9/2)+5(n-1)}:{2*(15/2)+9(n-1)}

= [(n/2){2*(9/2)+5(n-1)}]:[(n/2){2*(15/2)+9(n-1)}]
hence nth terms will be in the ratio
T(1,n):T(2,n)= [(9/2)+5(n-1)]:[(15/2)+9(n-1)]

=>T(1,13):T(2,13)=[(9/2)+5(13-1)]:[(15/2)+9(13-1)]
=(129/2):(231/2)
=43/77

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