Answer:
[tex]a_1=4[/tex]
[tex]a_n=(-1)^{n-1}4^n[/tex]
Step-by-step explanation:
Given a G.P series i.e geometric sequence
4, −16, 64, −256, ...
We have to find the recursive rule for the geometric sequence.
We know that [tex]a_1[/tex] is the first term of the sequence.
Here [tex]a_1=4[/tex]
As, the nth term of Geometric progression is
[tex]a_n=ar^{n-1}[/tex] where r is the common ratio
[tex]\text{Common ratio=r=}\frac{a_2}{a_1}=\frac{-16}{4}=-4[/tex]
Hence the recursive formula is
[tex]a_n=ar^{n-1}=4(-4)^{n-1}=(-1)^{n-1}4^n[/tex]
