[tex] a_n=\left\{\begin{array}{ccc}a_1=-64\\a_{n+1}=a_n:4\end{array}\right\\\\check:\\a_1=-64\\a_2=a_1:4\to a_2=-64:4=-16-OK\\a_3=a_2:4\to a_2=-16:4=-4-OK\\a_4=a_3:4\to a_4=-4:4=-1-OK\\\vdots [/tex]
Answer:
Step-by-step explanation:
A geometric sequence is defined as the sequence of number that follows a pattern were the next term is found by multiplying by a constant called the common ratio say r.
The recursive rule is given by;
[tex]a_n = r \cdot a_{n-1}[/tex] where n is the number of terms.
Given the sequence: [tex]-64, -16, -4 , -1, ....[/tex]
This sequence is a geometric sequence with common ratio (r) = [tex]\frac{1}{4}[/tex]
Here, first term [tex]a_1 = -64[/tex]
Since,
[tex]\frac{-16}{-64} = \frac{1}{4}[/tex]
[tex]\frac{-4}{-16} = \frac{1}{4}[/tex] and so on....
The recursive rule for this sequence is;
[tex]a_n = \frac{1}{4} \cdot a_{n-1}[/tex]
