Write the explicit formula for the geometric sequence.
64, 32, 16, 8, ...
The explicit formula for the geometric sequence 64, 32, 16, 8, ... is given by:
an = 64 * (1/2)^(n-1)
where a1 = 64 is the first term, and n represents the position of the term in the sequence.
To find the explicit formula for a geometric sequence, we need to determine the common ratio, denoted as 'r', and the first term, denoted as 'a1'.
In this case, if we divide each term by the previous term, we get a constant value of 1/2, indicating that the common ratio 'r' is 1/2.
Now, we can determine the first term 'a1' by inspecting the given sequence. The first term is 64.
Putting it all together, the explicit formula for this geometric sequence is:
an = a1 * r^(n-1)
Substituting the values we found:
an = 64 * (1/2)^n-1