Question

Calcule a soma da p.a. (-16,-14,-2,....84)

Answer 1

Se $a1 = - 16$ e $an = 84$ , temos:

$r = a_2 - a_1 \\ r = -14 - (-16)\\ r = -14 + 16\\r=2. \\ a_n = a_1 + (n-1)\times 2 \\ 84 = -16 + 2n -2 \\ 84 = -18 \times 2n \\ 84 + 18 = 2n \\ n = 102 / 2 \\ n = 51.$

Calculando a soma dos termos, teremos: 
$S_n = (a_1 + a_n)\times n / 2 \\ S_n = (-16 + 84)\times 51 / 2 \\ S_n = 68 \times 51 / 2 \\ S_n = 34 \times 51 \\ S_n = 1734.$

Bons estudos!