The third and sixth terms of a geometric sequence are -75 and -9375 respectively. Find the first term, the common ratio, and an explicit rule for the nth term.

Answer 1

t3 = ar^2 = -75
t6 = ar^5 = -9375
divide them
r^3 = 125
r = 5

in ar^2 = -75
a(25) = -75
a = -3

term(n) = -3(5)^(n-1)