Question

considere a progressão aritmética tal q a30 = 200 e a razao =7 qual a soma dos 30 primeiros termos dessa progressão

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Termo\,geral\,da\,PA\,em\,func_{\!\!,}\tilde ao}\\\underline{\rm da\,raz\tilde ao\,e\,do\,1^o\,termo}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf a_n=a_1\!+\!(n-1)\!\cdot r}}}}\\\\\underline{\rm Soma\,dos\,termos\,da\,PA}\\\\\Huge\boxed{\boxed{\boxed{\boxed{\sf S_n=\dfrac{n\!\cdot\!(a_1+a_n)}{2}}}}}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf a_{30}=a_1+29r\\\sf 200=a_1+29\cdot7\\\sf a_1+203=200\\\sf a_1=200-203\\\sf a_1=-3\\\sf S_{30}=\dfrac{30\cdot(-3+200)}{2}\\\\\sf S_{30}=\dfrac{30\cdot197}{2}=\dfrac{5910}{2}=2955\end{array}}$