Question

Calcule a soma dos 60 primeiros termos de P.A, sabendo que a21+a40=80 ​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf A~soma\,de\,dois\,termos\,equidistantes\,dos\,extremos}\\\underline{\sf \acute e\,igual\,a\,soma\,dos\,extremos.}\\\sf a_{21}+a_{40}=80\\\sf a_{21}+a_{40}=a_1+a_n\implies a_1+a_{60}=80\\\sf S_{60}=\dfrac{\diagdown\!\!\!\!\!\!60\cdot(a_1+a_{60})}{\diagdown\!\!\!2}\\\sf S_{60}=30\cdot80\\\sf S_{60}=2400\end{array}}$