Complete the resursive of the geometric sequence 10,6,3.6,2.16

a(n) = (3/5)a(n-1), where a(1) = 10 and n is 2 or greater.

Step-by-step explanation:

First determine the common factor.  Note that mult. the first term (10) by 3/5 results in the given second term (6); the third term is 3/5 of the second term (6), resulting in 18/5 (equivalent to 36/10 or 3.6/1, or just 3.6.  And so on.

Thus, a(n) = (3/5)a(n-1).  We can demo that this "works" for the fourth term:

the third term is 3.6, which, if mult. by (3/5), produces 2.16, as expected.

Thus, the recursive formula for this geometric sequence is a(n) = (3/5)a(n-1).

This is good only for a(1) = 10 and n = {2, 3, }

 a(1) = 10

 a(n) = a(n-1)·0.6