The geometric sequence with a fifth term of 1/3 and a constant ratio of 1/3 is Tn = (1/3)^-4 * (1/3)^n
The given parameters are:
Fifth term, T5 = 1/3
Constant ratio, r = 1/3
The nth term of a geometric sequence is
Tn = T1 * r^(n-1)
Substitute the known values in the above equation
1/3 = T1 * 1/3^4
Divide both sides by 1/3^4
T1 = (1/3)^-3
Substitute T1 = (1/3)^-3 in Tn = T1 * r^(n-1)
Tn = (1/3)^-3 * r^(n-1)
Substitute r = (1/3) in (1/3)^-3 * r^(n-1)
Tn = (1/3)^-3 * (1/3)^(n-1)
This gives
Tn = (1/3)^-4 * (1/3)^n
Hence, the geometric sequence with a fifth term of 1/3 and a constant ratio of 1/3 is Tn = (1/3)^-4 * (1/3)^n
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