math
posted by liza .
the third term of a geometric sequence is t3= 75 and the sixth term is t6= 9375. determine the first term and the common ratio

For a geometric series,
the nth term is
t(n)=ar^{n}
So
t(3)=ar³
t(6)=ar^{6}
t(6)/t(3)
= ar^{6} / ar³
= r^{63}
= r³
Solve for r in
r³=9375/(75)
r=(125)^{1/3}
=5
A = t(3)/r³
= 75/(5)³
= 3/5
and first term
= t(1)
= Ar
= 3/5(5)
= 3