Question

dada a p.a (3, 7, 11,...) finita, qual é a soma dos 5 primeiros termos

Answer 1

$\mathtt{R = A_2 - A_1} \\ \mathtt{R = 7 - 3} \\ \mathtt{R =4 }$

$\mathtt{A_n =A_1 + (n-1)~.~R} \\ \mathtt{A_5= 3+ (5-1)~.~4} \\ \mathtt{A_5= 3 + 4 ~.~4} \\ \mathtt{A_5 = 3 + 16} \\ \mathtt{A_5 = 19}$

$\mathtt{S_n = \dfrac{(A_n + A_1)~.~n}{2}} \\ \\ \\ \mathtt{S_5 = \dfrac{(19 +3)~.~4}{2}~~=~~\dfrac{22~.~5}{2}~~=~~\dfrac{110}{2}~~=~~55}$

Answer 2

$r = a_2 - a_1 = 7 - 3 = 4 \\ \\ a_5 = a1 + 4r = 3 + 4.4 = 19 \\ \\ S_5 = \frac{(a_1 + a_5).5}{2} \\ \\ S_5 = \frac{(3 + 19).5}{2} \\ \\ S_5 = \frac{110}{2} = 55$