Question

Qual a soma dos termos da P.A .( - 6, - 9, - 12 ,..., - 66)?

Answer 1

$\large\boxed{\begin{array}{l}\rm (-6,-9,-12\dotsc-66)\\\tt dados\begin{cases}\tt a_1=-6\\\tt a_n=-66\\\tt r=-9-(-6)=-9+6=-3\\\tt n=?\end{cases}\\\rm a_n=a_1+(n-1)\cdot r\\\rm -66=-6+(n-1)\cdot -3\\\rm -66=-6-3n+3\\\rm 3n=3-6+66\\\rm 3n=63\\\rm n=\dfrac{63}{3}\\\\\rm n=21\\\underline{\sf A\,soma\,dos\,termos\,\acute e}\\\\\sf S_{21}=\dfrac{21\cdot(-66-6)}{2}\\\\\sf S_{21}=\dfrac{21\cdot-\diagdown\!\!\!\!\!\!72}{\diagdown\!\!\!2}\\\\\sf S_{21}=21\cdot-36\\\rm S_{21}=-756\end{array}}$