I have tried solving this question using two different methods- "If the ratio of the sum of the first n terms of two APs is (7n+1) : (4n+27), then what is the ratio of their 9th terms?"

=>The first method

In this case the answer is 24/19.

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=>Second method

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In the second method i used this formula an=S_n-S(n-1) So For the first A.P. Sum of "n" terms =(7n+1)*x [using the formula] So, a9=S_9-S(8) We will finally get a_9=7x Similarly ,for the second A.P. we will have A_9=4x So,Ratio of the ninth term of both the A.P is 7:4(Check attachment for more!)

I want to know why am i getting two different answers?Are both the methods correct?IF NOT,then please ELABORATE why?

I will be thankful for help!

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