Question

Numa P. A. a soma do quarto com o nono termo é 8 e a soma do setimo com o decimo-segundo é 20. Calcule o Valor do primeiro termo

Answer 1

$a_n = a_1 + r(n-1)$

$a_4 + a_9 = 8 \iff a_1 + r\times 3+a_1 + r\times 8 = 8 \iff 2\times a_1 + 11\times r = 8$

$a_7 + a_{12} = 20 \iff a_1 + r\times 6+a_1 + r\times 19 = 20 \iff 2\times a_1 + 25\times r = 20$

$\left \{ {{2\times a_1 + 11\times r = 8} \atop {2\times a_1 + 25\times r = 20}} \right.$

$14\times r = 12 \iff r = \frac{6}{7}$

$2\times a_1 + 11\times \frac{6}{7} = 8 \iff 14\times a_1 + 66 = 56 \iff a_1 = \frac{-5}{7}$