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The sum of n terms of two APs is in the ratio$\; 5n + 1: 4n+10$. Find the ratio of their $\;5^{th}$ terms.


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Answer : (b) 1
Explanation : $\frac{S_{1}}{S_{2}}=\frac{n/2\;[2a_{1}+(n-1)d_{1}]}{n/2\;[2a_{2}+(n-1)d_{2}]}$
For the ratio of the $\;5^{th}\;$ term , $\;\frac{a_{1}+4d_{1}}{a_{2}+4d_{2}}$
Let $\;\frac{n-1}{2}=4\quad\;then\;n=8+1=9$
Replacing the value of n in the ratio ,
answered Jan 18, 2014 by yamini.v

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