Question

What is the recursive rule for the sequence? 3, −1, 1/3, −1/9, ...

Answer 1

Answer:

Step-by-step explanation:

(-1/9) /(1/3) = (1/3)/(-1) = -1/3....the common ratio of geometric  sequence  

the recursive rule is :

the nth term is :  An =A1 × r^(n-1)

r : the common ratio  

A1 ; the first term

r  = -1/3  and A1 =  3

An =3 ×(-1/3)^(n-1)

Answer 2

$\displaystyle a_1=-3\\r=-\dfrac{1}{3}\\a_n=a_{n-1}\cdot \left(-\dfrac{1}{3}\right)=-\dfrac{1}{3}a_{n-1}\\\\\\{\begin{cases}a_1=-3\\a_n=-\dfrac{1}{3}a_{n-1}\end{cases}}$