Secuencia entera de escuela primaria

a1+a1q^3=18

a1(1+q^3)=18

a1=18/(1+ q^3)

[q≦-1]

a2+a3=12

a1q+a1q^2=12

a1(q+q^2)=12

a1=12/(q+q^2)

[q≦-1]

18/ (1+q^3)=12/(q+q^2)

3q+3q^2=2+2q^3

2(1+q^3) -3(q+q^2)=0

2(1+q)(1-q+q^2)-3q(1+q)=0

( 1+q)(2-2q+2q^2-3q)=0

(1+q)(2q^2-5q+2)=0

(1+ q)(q-2)(2q-1)=0

q es un número entero.

Entonces q-2=0 q=2.

a1=12/(q+q^2)=12/6=2

s8=a1*(1-q^8)/(1-q)=2 *(1-2^8)/(1-2)=2*127=254