Question

2) Sabendo que a sequência (6,14-x, 18,...) é uma P.A., determine a soma dos 120 primeiros termos dela.

Answer 1

$\large\boxed{\begin{array}{l}\rm (6,14-x,18)~S_{120}=?\\\rm a_3=a_1+2r\longrightarrow r=\dfrac{a_3-a_1}{2}\\\\\rm r=\dfrac{18-6}{2}=\dfrac{12}{2}=6\\\\\rm a_{120}=a_3+117r\\\rm a_{120}=18+117\cdot6\\\rm a_{120}=18+702\\\rm a_{120}=720\\\rm S_{120}=\dfrac{\diagup\!\!\!\!\!\!\!120\cdot(6+720)}{\diagup\!\!\!\!2}\\\\\rm S_{120}=60\cdot726\\\rm S_{120}=43560\end{array}}$