Question

Interpolar 4 medios geometricos entre 5/3 y81/625

Answer 1

Tenemos.
Interpolar 4 medios geometricos

5/3:  - : - : - : - : 81/625
n = numero de termino = 6
a1 = 5/3
an = 81/625
Razon = r= ?

Formula para encontra la razon
r =n-1√(an/a1)

r = ⁶⁻¹√((81/625)/(5/3))
r = ⁵√((81*3)/(625*5))
r = ⁵√((3⁴*3)/(5⁴*5)
r = ⁵√(3⁵/5⁵) =
r = (3⁵/⁵ )/ (5⁵/⁵)
r = 3/5

La razon = 3/5

1er termino = 5/3
2do termino = 5/3 * 3/5 =(5*3)/(3*5) = 15/15 = 1
3er termino = 1* 3/5 = (1*3)/5 = 3/5
4to termino = 3/5 * 3*5= (3*3)/(5*5) = 9/25
5to termino = 9/25 * 3/5= (9*3)/(25*5) = 27/125
6to termino = 81/625

Respuesta.
La progresion
5/3: 1 : 3/5: 9/25: 27/125 : 81/625