Question

Calcule a soma dos 101 termos da pá ( 5,10,15)…

Answer 1

$\mathtt{R = A_2 - A_1} \\ \mathtt{R = 10 - 5 } \\ \mathtt{R = 5} \\ \\ \mathtt{A_n = A_1 + (n-1)~.~R} \\ \mathtt{A_{101}= 5 + (101-1) ~.~5} \\ \mathtt{A_{101}= 5 + 100 ~.~5} \\ \mathtt{A_{101}= 5 + 500} \\ \mathtt{A_{101}=505} \\ \\ \\ \mathtt{S_n = \dfrac{(A_n + A_1)~.~n}{2}} \\ \\ \\ \mathtt{S_{101} \dfrac{(505+5)~.~101}{2}~~=~~\dfrac{510~.~101}{2}~~=~~\dfrac{51.510}{2}~~=~~25.755}$