Question

interpole quatro meios geometricos entre -4 e 972

Answer 1

a_1 = - 4
a_n = 972
n = 4 + 2 ===> n = 6
q = ?

$a_n=a_1\cdot\,q^{n-1}\\\\972=-4\cdot\,q^5\\\\q^5=-243\\\\q^5=(-3)^5\\\\\boxed{q=-3}$
 
a_2 = a_1 . q =====> a_2 = (- 4) . (- 3) =====> a_2 = 12

a_3 = a_2 . q =====> a_3 = (12) . (- 3) =====> a_3 = - 36

a_4 = a_3 . q =====> a_4 = (- 36) . (- 3) =====> a_4 = 108

a_5 = a_4 . q =====> a_5 = (108) . (- 3) =====> a_5 = - 324