Question

Use the recursively defined geometric sequence a_1=5/6, a_n=4a_n−1 and find the common ratio

Answer 1

The recurrence gives a_n / a_{n-1} = 4, so the common ratio is 4.
(Thus a_n = (5/6)·4^{\,n-1}, e.g. a_2 = 20/6 = 10/3, a_3 = 40/3, ...)