Find the 10th term in the following geometric sequence.
8, 4, 2, 1, . . .
To find the 10th term in this geometric sequence, we need to determine the common ratio first. We can find the common ratio by dividing any term by the previous term.
The ratio between the second term (4) and the first term (8) is 4/8 = 1/2.
The ratio between the third term (2) and the second term (4) is 2/4 = 1/2.
The ratio between the fourth term (1) and the third term (2) is 1/2.
We can see that the common ratio is 1/2.
We can then find the tenth term by multiplying the first term by the common ratio raised to the power of (10 - 1). In this case, the first term is 8.
10th term = 8 * (1/2)^(10 - 1)
= 8 * (1/2)^9
= 8 * (1/512)
= 8/512
= 1/64
The 10th term in the sequence is 1/64.