Find the geometric sequence with

t(5)= -2
and
t(7)= -8

find a

How do I do this?

Well, a geometric sequence is of the form;

a, ar, a(r^2), a(r^3), ... , a(r^n)

where t(0) = a, t(1) = ar etc.

[the sequence 1, 1/2, 1/4, 1/8, 1/16,...
is geometric with a = 1 and r = 1/2]

Ok, hope that helps!