Question

Calcular a soma dos termos da P.A. (-16, -14, -12, ..., 84), sabendo que essa PA tem 51.

A 1734


B 1743


C 7134


D 7431


E 4371

Answer 1

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$\boxed{\begin{array}{l}\sf a_n=a_1+(n-1)\cdot r\\\sf 84=-16+(n-1)\cdot2\\\sf -16+2n-2=84\\\sf 2n=84+2+16\\\sf 2n=102\\\sf n=\dfrac{102}{2}\\\sf n=51\\\sf S_n=\dfrac{ n\cdot(a_1+a_n)}{2}\\\sf S_{17}=\dfrac{51\cdot(-16+84)}{2}\\\sf S_{51}=\dfrac{51\cdot\diagdown\!\!\!\!\!\!68^{17}}{\diagdown\!\!\!\!2}\\\sf S_{17}=51\cdot17\\\sf S_{17}=867\end{array}}$