The ratio of their $n$-th term. The sum of $n$ terms of two arithmetic series are in the ratio of $(7n+ 1) : (4n+ 27)$. We have to find the ratio of their $n$-th term.
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I tried to find the ratio by using the formula of summation of A.P.
But it becomes too long due to many variables that is $a_1,a_2,d_1,d_2$

We have $$\frac{7n+1}{4n+27}=\dfrac{\dfrac n2\{2a_1+(n-1)d_1\}}{\dfrac n2\{2a_2+(n-1)d_2\}}=\dfrac{a_1+\dfrac{(n-1)}2\cdot d_1}{a_2+\dfrac{(n-1)}2\cdot d_2}$$
Replace $\dfrac{n-1}2$ with $m-1\iff n=2m-1$ to find the ratio of their $m$th term.
