Question

The correctly answered answer will be marked as brainliest.​

Answer 1

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$\underline{\blacksquare\:\:\footnotesize{\red{SolutioN}}}$

$\footnotesize{\underline{given}}$

$\footnotesize{\text{The sum of first 'n' terms in an AP series}\:=3n-n^3}$

$\boxed{\footnotesize{i.e.,\:\:\:\:\:S_n=3n-n^3}}$

$\footnotesize{\therefore\:S_1=3(1)-(1)^3=2}$

$\footnotesize{\therefore\:S_2=3(2)-(2)^3=-2}$

$\footnotesize{\therefore\:common\: difference=d=S_2-S_1}$

$\footnotesize{\implies\:d=(-2)-(2)}$

$\footnotesize{\implies\:d= -4}$

$\footnotesize{\therefore\:first\:term=a_1=S_1=2}$

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$\therefore\:\:\:\footnotesize{a_2=a_1+(2-1)d}$

$\footnotesize{\implies a_2=2+(1)(-4)}$

$\footnotesize{\implies \red{\boxed{a_2=-2}}}$

$\therefore\:\:\:\footnotesize{a_3=a_1+(3-1)d}$

$\footnotesize{\implies a_3=2+(2)(-4)}$

$\footnotesize{\implies a_3=2-8}$

$\footnotesize{\implies \red{\boxed{a_3=-6}}}$

$\therefore\:\:\:\footnotesize{a_{10}=a_1+(10-1)d}$

$\footnotesize{\implies a_{10}=2+(9)(-4)}$

$\footnotesize{\implies a_{10}=2-36}$

$\footnotesize{\implies \red{\boxed{a_{10}=-34}}}$

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