For the following geometric sequence, find the 5th term in the sequence 0.125, 0.25, 0.5

To find the 5th term in the given geometric sequence, we first need to identify the common ratio. A geometric sequence is one in which each term is obtained by multiplying the previous term by a constant known as the common ratio.

The sequence provided is 0.125, 0.25, and 0.5. We can find the common ratio (r) by dividing the second term by the first term:

r = 0.25 / 0.125 = 2

Next, we can verify this by dividing the third term by the second term:

r = 0.5 / 0.25 = 2

Since the common ratio is consistent, we confirm that the common ratio (r) is indeed 2. Now, to find the 5th term of the sequence, we can use the formula for the n-th term of a geometric sequence, which is:

T_n = a * r^(n-1)

Here, a is the first term (0.125), r is the common ratio (2), and n is the term number we want to find (5).

Plugging these values into the formula:

T_5 = 0.125 * 2^(5-1) = 0.125 * 2^4 = 0.125 * 16 = 2

Therefore, the 5th term in the sequence is 2.