Question

Sabendo que o primeiro termo de uma PA vale 21 e a razão é -4, calcule a soma dos 41 primeiros termos dessa PA.​

Answer 1

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

$\large\boxed{\begin{array}{l}\sf a_1=21~~r=-4\\\sf a_{41}=a_1+4r\\\sf a_{41}=21+4\cdot(-4)\\\sf a_{41}=21-16\\\sf a_{41}=5\end{array}}$

$\Large\boxed{\begin{array}{l}\sf S_{41}=\dfrac{41\cdot(21+5)}{2}\\\\\sf S_{41}=\dfrac{41\cdot\diagdown\!\!\!\!\!\!26^{13}}{\diagdown\!\!\!\!2}\\\\\sf S_{41}=41\cdot13\\\sf S_{41}=533\end{array}}$