Use the recursively defined geometric sequence a1=5/6 , an=4an−1 and find the common ratio.

Answer 1

a1 = 5/6

By substituting n = 2 into the recursive formula, we have:

a2 = 4(a2-1)
a2 = 4(a1)
a2 = 4(5/6)
a2 = 20/6

Simplifying the fraction, we have:

a2 = 10/3

Now, let's find the ratio between the second term and the first term:

R = (a2)/(a1)
R = (10/3)/(5/6)
R = (10/3)*(6/5)
R = 60/15
R = 4

Therefore, the common ratio is 4.