To find the general term (un) of a geometric sequence, you need the value of any two terms in the sequence. In this case, we have u7 = 24 and u15 = 384.
The general term of a geometric sequence can be found using the formula:
un = u1 * r^(n-1)
where un is the nth term, u1 is the first term, r is the common ratio, and n is the position of the term in the sequence.
To find the common ratio (r), we can use the fact that the ratio of any two consecutive terms in a geometric sequence is constant.
First, we can find the value of u1. To do this, we need to find the common ratio (r) by using the given terms:
r = u15 / u7 = 384 / 24 = 16
Now, we can use the value of r to find u1:
u1 = u7 / r^(7-1) = 24 / 16^6
Simplifying the equation:
u1 = 24 / (2^4)^6 = 24 / 2^24
Thus, the general term of the sequence is:
un = (24 / 2^24) * 16^(n-1)
Note: The value of u1 can also be simplified further, but it depends on whether the question requires a simplified form or not.