Answer:
Recursive formula for the geometric sequence is, \(a_n =-4\cdot a_{n-1} \cdot\)
Step-by-step explanation:
A geometric sequence states that a sequence in which the ratio of any term to the previous term is constant.
A recursive formula states that it uses the preceding term to define the next term of the sequence.
For the geometric sequence, the recursive formula is given by;
\(a_n = a_{n-1} \cdot r\) where r is the common ratio.
Given the following:
\(a_1 = -2\), \(a_2 = 8\) and \(a_3 = -32\)
The common ratio for the geometric sequence , r =-4
Since,
\(\frac{a_2}{a_1} = \frac{8}{-2} = -4\)
\(\frac{a_3}{a_2} = \frac{-32}{8} = -4\) ..
Then, the recursive formula for the geometric sequence is,
\(a_n = a_{n-1} \cdot (-4)\)
or
\(a_n =-4\cdot a_{n-1} \cdot\)
