A geometric sequence is defined recursively by #a_n = 15a_(n-1)#, the first term of the sequence is 0.0001, how do you find the explicit formula for the nth term of the sequence?

1 Answer
Feb 21, 2016

Answer:

The explicit formula for the #n^(th)# term of the given geometric series is #0.0001*15^(n-1)#.

Explanation:

As the geometric sequence is defined recursively by #a_n=15a_(n−1)# and the first term of the sequence is #0.0001#, it is obvious that the ratio of a term divided by its preceding term is #15#, that if written in general form of geometric series #{a, ar, ar^2, ar^3,....}#, #a# is #0.0001# and #r=15#.

As the #n^(th)# term of geometric series is #ar^(n-1)#, hence the explicit formula for the #n^(th)# term of the given geometric series is #0.0001*15^(n-1)#.