A certain infinite geometric series has first term 7 and sum 4. What is the result when the third term is divided by the second term?

This is an "alternating" series ... we have

4 = 7/ [1 - (- r)]  = 7/(1 + r)   and solving for r, we have

4 = 7 / (1 + r) → (1 + r) = 7/4 → r = 3/4

And the form of this series is ..  ∑ 7 *(-3/4)^(n-1)   from 1 to infinity

And the result of dividing the third term by the second term is just (-3/4)  .... as we would expect....!!!!