Question

Qual é a soma de todos os naturais,múltiplos de 3,entre 1 e 1000?

Answer 1

$\boxed{\begin{array}{l}\sf(3,6,9...999)\\\sf a_n=a_1+(n-1)\cdot r\\\sf999=3+(n-1)\cdot3\\\sf \diagdown\!\!\!3+3n-\diagdown\!\!\!3=999\\\sf n=\dfrac{999}{3}\\\sf n=333\\\sf S_{333}=\dfrac{333\cdot(3+999)}{2}\\\sf S_{333}=\dfrac{333\cdot1002}{2}\\\sf S_{333}=333\cdot501\\\sf S_{333}=166833\end{array}}$