Question

intr-o progresie geometrica avem a2=5 si a5=40.Determinati a1

Answer 1

[tex]\text{Voi nota ratia cu q.}\\ \left \{ {{a_2=5} \atop {a_5=50}} \right.\Leftrightarrow \left \{ {{a_1\cdot q=5} \atop {a_1\cdot q^4=40}} \right.\\ \text{Daca facem raportul celor doua relatii vom obtine:}\\ \dfrac{a_1\cdot q}{a_1\cdot q^4}=\dfrac{5}{40} \Rightarrow \dfrac{1}{q^3}=\dfrac{1}{8}\Rightarrow q^3=8,\text{deci}\ q=2\\ a_1\cdot 2=5\\ a_1=\dfrac{5}{2}[/tex]