Let a_1,a_2,a_3, ... ... . be an A.P. Ifn fraca_1 + a_2 + ... + a_10a_1 + a_2 + ... + a_p = frac100p^2,n p ≠ 10, then fraca_11a_10 is equal to

(c): We have,n fraca_1 + a_2 + ... + a_10a_1 + a_2 + ... + a_p = frac100p^2n nn\[ n => fracS_10S_p = frac100p^2 => S_p = fracS_10 * p^2100\ (i) n ]nnNow,nfraca_11a_10 = fracS_11 - S_10S_10 - S_9 = fracfracS_10(11)^2100 - S_10S_10 - fracS_10 * (9)^2100 n[Using (i)]nn= frac11^2 - 100100 - 9^2 = (21 / 19)

Let a_{1},a_{2},a_{3}, be an A.P. If \frac{a_{1} + a_{... | Sequence & Series (Mathematics)

(c): We have,\n

\frac{a_{1} + a_{2} + \ldots + a_{10}}{a_{1} + a_{2} + \ldots + a_{p}} = \frac{100}{p^{2}}

\n\end{enumerate}\n\n\[\begin{matrix}\n \Rightarrow \frac{S_{10}}{S_{p}} = \frac{100}{p^{2}} \Rightarrow S_{p} = \frac{S_{10} \cdot p^{2}}{100}\#(i) \\\n\end{matrix}\]\n\nNow,\n

\frac{a_{11}}{a_{10}} = \frac{S_{11} - S_{10}}{S_{10} - S_{9}} = \frac{\frac{S_{10}(11)^{2}}{100} - S_{10}}{S_{10} - \frac{S_{10} \cdot (9)^{2}}{100}}

\\\n{[}Using (i){]}\n\n

= \frac{11^{2} - 100}{100 - 9^{2}} = \frac{21}{19}

Explanation

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