Question

answer the marked question..............​

Answer 1

               

Answer: (14m - 6) : (8m + 23)

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Cool question. Answered similar question morning.

Given that,

$\boxed{\sf{S1_n:S2_n=(7n+1):(4n+27)}}$

We know that,

$\boxed{\sf{S_n=n \times T_{[\frac{n+1}{2}]}}}\ = \ \boxed{\sf{S_n=n \times [\frac{n+1}{2}]^{th}\ term}}$

So, let me take,

$\boxed{\sf{n=2m-1}}$

(You'll get later why I took n=2m-1. If won't, plz ask me. )

$\boxed{\sf{S1_{2m-1}:S2_{2m-1}=(7(2m-1)+1):(4(2m-1)+27)}} \\ \\ \\ \boxed{\sf{(2m-1)[T1_{\frac{2m-1+1}{2}}]:(2m-1)[T2_{\frac{2m-1+1}{2}}]=(14m-7+1):(8m-4+27)}} \\ \\ \\ \boxed{\sf{T1_{\frac{2m}{2}}:T2_{\frac{2m}{2}}=(14m-6):(8m+23)}} \\ \\ \\ \boxed{\sf{T1_m:T2_m=\bold{(14m-6):(8m+23)}}}$

∴ Ratio of mth terms is (14m - 6) : (8m + 23).

Hope this helps. ^_^

Please ask me if you have any doubt in my answer.

Mark this answer as the brainliest. This is the simplest method for such questions.

Thank you. :-))