Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 5 and 625, respectively.

Answer 1

We can wite the second term as a1r  and 5th term as a1r^4  where a1 = first term and r = common ratio.

so (a1r^4) / (a1r) = r^3  = 625/5

r^3 = 125

r = 5  

so a1* 5 = 5  giving  a1 = 1


explicit rule is an =  5^(n-1)