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Question

The ratio of the sum of first $$n$$ terms of two APs is $$(7n + 1) : (4n + 27)$$. Find the ratio of their $$mth$$ terms.


Solution

$$\dfrac{{\dfrac{n}{2}\left[ {2{a_1} + \left( {n - 1} \right){d_1}} \right]}}{{\dfrac{n}{2}\left[ {2{a_2} + \left( {n - 1} \right){d_2}} \right]}} = \dfrac{{7n + 1}}{{4n + 27}}$$

$$\dfrac{{2{a_1} + \left( {n - 1} \right){d_1}}}{{2{a_2} + \left( {n - 1} \right){d_2}}} = \dfrac{{7n + 1}}{{4n + 27}}$$
if $$n=17$$

$$\dfrac{{2{a_1} + 16{d_1}}}{{2{a_2} + 16{d_2}}} = \dfrac{{120}}{{95}} = \dfrac{{24}}{{19}}$$

$$\dfrac{{{a_1} + 8{d_1}}}{{{a_2} + 8{d_2}}} = \dfrac{{24}}{{19}}$$

Mathematics

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