The sequence given is 64, 16, 4. To find the 10th term, let’s first determine the pattern of the sequence.
If we look closely, we can see that each term is obtained by dividing the previous term by 4:
- 64 ÷ 4 = 16
- 16 ÷ 4 = 4
This tells us that the sequence follows a geometric progression where the first term (a) is 64, and the common ratio (r) is 1/4 (or 0.25).
The formula for the nth term of a geometric sequence is given by:
T(n) = a * r^(n-1)
Now, to find the 10th term (T(10)), we plug the values into the formula:
T(10) = 64 * (1/4)^(10-1)
This simplifies to:
T(10) = 64 * (1/4)^9
T(10) = 64 * (1/262144)
T(10) = 64 / 262144
T(10) = 1 / 4096
Thus, the 10th term of the sequence is 1/4096.