Answer:
6561/131072
Step-by-step explanation:
You want the 10th term of the geometric sequence that begins 2/3, 1/2, 3/8, ...
Ratio
The common ratio of the sequence is ...
(1/2)/(2/3) = 3/4
(3/8)/(1/2) = 3/4
N-th term
The n-th term is given by ...
an = a1·r^(n -1) . . . . . . . . where a1 is the first term and r is the ratio
The 10th term will be ...
a10 = (2/3)(3/4)^10 -1) = 6561/131072
The tenth term of the sequence is 6561/131072.
