Let Sₙ and sₙ deontes sum of first n terms of two different A.P . for which frac{{{sₙ}}}

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8. Sequences and Series

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Let $S_n$ and $s_n$ deontes the sum of first $n$ terms of two different $A.P$. for which $\frac{{{s_n}}}{{{S_n}}} = \frac{{3n - 13}}{{7n + 13}}$ then $\frac{{{s_n}}}{{{S_{2n}}}}$

A

$\frac{{3n - 13}}{{14n + 26}}$

B

$\frac{{6n - 26}}{{17n + 13}}$

C

$\frac{{3n - 13}}{{28n + 26}}$

D

None

Solution

$\mathrm{s}_{\mathrm{n}}=\lambda\left(3 \mathrm{n}^{2}-13 \mathrm{n}\right)$

$\mathrm{s}_{\mathrm{n}}=\lambda\left(7 \mathrm{n}^{2}+13 \mathrm{n}\right)$

$\mathrm{s}_{2 \mathrm{n}}=\lambda\left(28 \mathrm{n}^{2}+26 \mathrm{n}\right)$

$\frac{s_{n}}{s_{2 n}}=\frac{7 n+13}{28 n+26}$

Standard 11

Mathematics

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