Question

Enter a recursive rule for the geometric sequence.

Answer 1

Answer:

a1= 4  an= -4a _n-1

Step-by-step explanation:

just took the k12 test

Answer 2

Answer:

$a_1=4$

$a_n=(-1)^{n-1}4^n$

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  $a_1$ is the first term of the sequence.

Here $a_1=4$

As, the nth term of Geometric progression is

$a_n=ar^{n-1}$ where r is the common ratio

$\text{Common ratio=r=}\frac{a_2}{a_1}=\frac{-16}{4}=-4$

Hence the recursive formula is

$a_n=ar^{n-1}=4(-4)^{n-1}=(-1)^{n-1}4^n$