Answer:
Option D is correct.
Explicit formula for the geometric sequence is, [tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]
Step-by-step explanation:
Geometric sequence states that a sequence of numbers in which the ratio between consecutive terms is constant,
we can write a formula for the nth geometric sequence in the form of:
[tex]a_n = a_1r^{n-1}[/tex] .....[1] where [tex]a_1[/tex] is the first term and r is the common ratio between successive term.
Given the sequence: 64, 32, 16 , 8......
Here, first term ([tex]a_1[/tex]) = 64.
Common ratio(r) = 0.5
Since,
[tex]\frac{32}{64} =0.5[/tex]
[tex]\frac{16}{32} = 0.5[/tex] ,
[tex]\frac{8}{16} = 0.5[/tex] ......
Substitute the value of a and r in [1] we get;
[tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]
therefore, the explicit formula for the geometric sequence is, [tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]
