Answer:
[tex]d(1)=-1.5[/tex] and recursive formula is [tex]d(n)=d(n-1)\cdot (-4)[/tex].
Step-by-step explanation:
The given geometric sequence is
[tex]-1.5, 6, -24, 96,...[/tex]
Here, the first term is -1.5. So
[tex]d(1)=-1.5[/tex]
Second term is 6. So,
[tex]d(2)=6[/tex]
In the given geometric sequence, the common ratio is
[tex]r=\dfrac{d(2)}{d(1)}=\dfrac{6}{-1.5}=4[/tex]
The recursive formula of the geometric sequence is
[tex]d(n)=d(n-1)\cdot r[/tex]
where r is common ratio.
[tex]d(n)=d(n-1)\cdot (-4)[/tex]
Therefore, the recursive formula is [tex]d(n)=d(n-1)\cdot (-4)[/tex].
