Question

Calcular a soma dos termos da P.A (-16,-14,-12,...,84)

Answer 1

$a_{1}=-16 \\ a_{2}=-14$

$r=a_{2}-a_{1}=-14-(-16)=-14+16=2$

$a_{n}=a_{1}+(n-1)r \\ a_{n}=-16+(n-1)2 \\ a_{n}=-16+2n-2 \\ a_{n}=2n-18 \\ 84=2n-18 \\ 84+18=2n \\ 2n=102 \\ n=102/2 \\ n=51$

$S_{n}=(a_{1}+a_{n})*n/2 \\ S_{51}=(a_{1}+a_{51})*51/2 \\ S_{51}=(-16+84)*51/2 \\ S_{51}=68*51/2 \\ S_{51}=34*51 \\\\\boxed{\boxed{S_{51}=1734}}$