Answer:
1/6, 1/3, 2/3
Step-by-step explanation:
Given data:
The sum of the first three terms of a finite geometric series is7/6 and their product 1/27 is .
Let a/r , a and ar be the three terms of a finite geometric series then:
a/r + a + ar = 7/6
and
(a/r) x (a) x (ar) = 1/27
Now first solving for a:
solving second equation
a^3r/r = 1/27
a^3= 1/27
a = 1/[tex]\sqrt[3]{27}[/tex]
a=1/3
Now solving for r:
Solving first equation
a/r + a + ar = 7/6
Putting value of a= 3 in above equation
1/3r + 1/3 + r/3 = 7/6
(1+r+r^2)/3r= 7/6
6(1+r+r^2)= 7(3r)
6+ 6r+ 6r^2= 21r
6r^2 - 15r +6=0
r=2
Hence the first three terms of a finite geometric series are
a/r= (1/3)/(2)
= 1/6
a= 1/3
ar= 1/3 (2)
=2/3 !
