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
Shwetank Mauria
Feb 21, 2016

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).

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