Answer:
The required recursive formula is:
\(a_n=(-3)\times a_{n-1}\)
Step-by-step explanation:
We are given a geometric sequence as:
6,-18,54,-162,.....
Clearly after looking at different terms of the sequence we could observe that the sequence is an geometric progression (G.P.) with common ratio= -3 denoted by r.
Let \(a_n\) represents the nth term of the sequence.
This means that:
\(a_1=6, a_2=-18, a_3=54, a_4=-162,......\)
As the common ratio is -3.
so,
\(a_1=6\\\\a_2=-18=(-3)\times a_1\\\\a_3=54=(-3)\times a_2\\\\.\\.\\.\\.\\.\\.\\.\\.\\.a_n=(-3)\times a_{n-1}\)
Hence, the required recursive formula for the geometric sequence is:
\(a_n=(-3)\times a_{n-1}\)