Question

найдите a1 и q геометрической прогрессии если : a4-a2=18, a5-a3=36

Answer 1

$a_{4}-a_{2}=a_{1}q^3-a_{1}q=a_{1}q(q^2-1)=18\ a_{5}-a_{3}=a_{1}q^4-a_{1}q^2=a_{1}q^2(q^2-1)=36\ q^2-1=frac{18}{a_{1}q}\ a_{1}q^2*frac{18}{a_{1}q}=36\18q=36\q=2\a_{1}=3$