SOLUTION: what is the 11th term of the geometric sequence 81,-27,9?

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Question 571200: what is the 11th term of the geometric sequence 81,-27,9?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
looks like the common ratio is -1/3.
81 * -1/3 = -27 * -1/3 = 9, etc.
An = A1*r^(n-1) i believe.
first term is A1 which is equal to 81.
second term is 81 * -(1/3)^1 = -27
third term is 81 * -(1/3)^2 = 9
the 11th terms should be:
81 * -(1/3)^10 = .001371742
as a fraction it would be equal to:
81 * -(1/3)^10 which is equal to:
81 * (-1)^10 / 3^10 which is equal to:
81 * 1 / 59049 which is equal to:
81 / 59049
the decimal equivalent of 81 /59049 is equal to .001371742.
if you were to explicitly analyze the sequence, you would get the following table.
sequence number       number
1                      81
2                      -27
3                       9
4                       -3
5                       1
6                       -1/3
7                       1/9
8                       -1/27
9                       1/81
10                      -1/243
11                      1/729

note that 1/729 is equivalent to 81 / 59049
multiply 1/729 by 81 / 81 and you get 81 / 59049