Answer:
a4 = -3 * 4^(4-1) = -3 * 4^3 = -3*64 = -192
Explanation:
A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is always the same. In this case, the given sequence is -3, -12, -48, -192, -768.
To find the explicit formula for this geometric sequence, we can use the following formula:
an = a1 * r^(n-1)
where:
a1 is the first term in the sequence (-3)
an is the nth term in the sequence
r is the common ratio (the ratio between any two consecutive terms)
To find the common ratio, we can divide -12 by -3, -48 by -12, -192 by -48, and -768 by -192, and in all cases we get r = 4
Therefore, the explicit formula for this geometric sequence is:
an = -3 * 4^(n-1)
This formula can generate any term of the sequence given the value of n.
So, for example, the fourth term of the sequence, -192, can be obtained by inputting n = 4 in the explicit formula:
a4 = -3 * 4^(4-1) = -3 * 4^3 = -3*64 = -192