Question

Calcule a soma dos 15 primeiros termos da P.A. (-45,-41,-37,-33,....)?

Answer 1

Olá Alice!!

 

P.A. (-45,-41,-37,-33,....)     a razão é  R = -41-(-45) >>>> R = 3.

 

 

$A_{n}=A_{1}+(n-1)R$

 

$A_{15}=A_{1}+(15-1)3$

 

$A_{15}=-45+(14)3$

 

$A_{15}=-45+42$

 

$\boxed{\boxed{A_{15}=-3}}$

 

 

Agora podemos calcular a Soma do 15 termos:

 

$S_{n}=(A_{1}+A_{n}).\frac{n}{2}$

 

$S_{15}=(A_{1}+A_{15}).\frac{15}{2}$

 

$S_{15}=(-45+(-3)).\frac{15}{2}$

 

$S_{15}=\frac{-48.15}{2}$

 

$S_{15}=-24.15$

 

$\large{\boxed{\boxed{S_{15}=-360}}}$

 

veja se entendeu