Question

Calcule a soma dos 72 primeiros termos da PA (3,9,...)

Answer 1

Resposta:

$S_{72} =15\ 552$

Explicação passo a passo:

$a_{1} =3\\\\a_{2} =9\\\\r=a_{2} -a_{1} =9-3=6\\\\n=72\\\\\\\\a_{n} =a_{1} +(n-1)r\\\ \Rightarrow\ a_{72} =3+(72-1)6\\\ \Rightarrow\ a_{72} =3+(71)6\\\ \Rightarrow\ a_{72} =3+426\\\ \Rightarrow\ a_{72} =429\\\\\\S_{n} =\frac{(a_{1}+a_{n} )n}{2} \\\\\ \Rightarrow\ S_{72} =\frac{(3+429)72}{2} \\\\\ \Rightarrow\ S_{72} =(432)36\\\\\ \Rightarrow\ S_{72} =15\ 552$