Question

Qual o valor de a soma : a + 2a + 3a + .... 39a+ 40a = 4100

Answer 1

$S_n=\frac{(a_1+a_n)n}{2}\\\\S_{40}=\frac{(a+40a)40}{2}\\\\S_{40}=41a\cdot20\\\\S_{40}=820a$

 Daí,

$\underbrace{a+2a+3a+...+40a}_{820a}=4100\\\\820a=4100\\\\\boxed{a=5}$