amro1234
contestada

In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an. Then write the first three terms of the sequence.

Respuesta :

LammettHash
[tex]a_4=ra_3[/tex]
[tex]a_5=ra_4=r^2a_3[/tex]
[tex]a_6=ra_5=r^3a_3[/tex]

[tex]40=-5r^3\implies r^3=-8\implies r=-2[/tex]

[tex]a_3=ra_2=r^2a_1[/tex]

[tex]-5=(-2)^2a_1\implies a_1=-\dfrac54[/tex]

You know the first and third terms, [tex]a_1[/tex] and [tex]a_3[/tex], so you just need to find the second term [tex]a_2[/tex]:

[tex]a_2=ra_1\implies a_2=-2\left(-\dfrac54\right)=\dfrac52[/tex]

Otras preguntas