Question

Calcule a soma dos primeiros n termos da progressão aritmética, se:

a₁= -1
r= -8
n=20​

Answer 1

$\large\boxed{\begin{array}{l} \sf{a_{20} = - 1 + (20 - 1) \cdot( - 8)} \\ \sf{ a_{20} = - 1 + ( - 152) } \\ \sf{ a_{20} = - 153} \\ \\ \sf{S _{20} = \dfrac{ - 1 + ( - 153)}{2} \cdot20 } \\ \\ \sf{S _{20 } = - 77 \cdot20} \\ \\ \boxed{ \boxed{ \sf{S _{20} = - 1540}}} \checkmark\end{array}}$

Answer 2

Primeiro vamos achar o a₂₀:

$\sf a_n=a_1+(n-1)\cdot r$

$\sf a_{20}=-1+(20-1)\cdot(-8)$

$\sf a_{20}=-1+19\cdot(-8)$

$\sf a_{20}=-1-152$

$\boxed{\boxed{\sf a_{20}=-153}}$

Agora vamos achar a soma dos 20 primeiros termos:

$\sf S_n=\dfrac{(a_1+a_n)\cdot n}{2}$

$\sf S_{20}=\dfrac{(-1+(-153))\cdot 20} {2}$

$\sf S_{20}=\dfrac{(-1-153)\cdot20}{2}$

$\sf S_{20}=\dfrac{-154\cdot20}{2}$

$\sf S_{20}=-77\cdot20$

$\boxed{\boxed{\sf S_{20}=-1540}}\leftarrow\textsf{resposta}$