Answer:
Step-by-step explanation:
Givens
a = 2187
r = 1/3
L = 1/9
what is n
Formula
L = a*r^(n-1)
1/9 = 2187 * (1/3)^(n-1)
1/(9 * 2187) = (1/3)^(n - 1)
1/19683 = (1/3)^(n - 1)
=================
You need to break 19683 down into its prime factors.
19683 = 3* 729
19683 = 3 * 3 * 243
19683 = 3 * 3 * 3 * 81
81 = 3^4 so there are 4 more threes in the breakdown.
19683 = 3 * 3 * 3 * 3 * 3 * 3 * 3
1/19683 = 1/(3)^(7-1)
1/9 is the 6th term in the series.