Question

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

Answer 1

Razão = -41 - (-45) = -41 + 45 = 4

Vamos agora achar o 15º termo:

$a_n=a_m+(n-m).razao\\\\a_{15}=a_1+(15-1)*4\\\\a_{15}=-45+14*4\\\\a_{15}= -45+56\\\\a_{15}=11\\\\\\Agora\;podemos\;achar\;a\;soma:\\S_n=\frac{(a_1+a_{n})n}{2}\\\\S_{15}=\frac{(a_1+a_{15})*15}{2}\\\\S_{15}=\frac{(-45+11)*15}{2}\\\\S_{15}=\frac{(-34)*15}{2}\\\\S_{15}=-17*15\\\\S{15}=-255$