Respuesta :
Answer:
Option A.
Step-by-step explanation:
The given sequence is 1.5, 3, 6............
We will check first whether the the given sequence is arithmetic or geometric.
For arithmetic sequence
[tex]a_{2}-a_{1}=3-1.5=1.5[/tex]
[tex]a_{3}-a_{2}=6-3=3[/tex]
1.5 ≠ 3, therefore, the given sequence is not an arithmetic sequence.
For geometric sequence
[tex]\frac{a_{2} }{a_{1} }=\frac{3}{1.5}=2[/tex]
[tex]\frac{a_{3} }{a_{2} }=\frac{6}{3}=2[/tex]
2 = 2, therefore, sequence is geometric.
For geometric sequence explicit formula is defined as
[tex]a_{n}=a_{1}(r)^{n-1}[/tex]
[tex]a_{7}=1.5(r)^{7-1}[/tex]
= [tex]1.5(2)^{6}=96[/tex]
Therefore, Option A. is the answer.
