Question

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

Answer 1

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=-(1)/(3)\\a_n=a_(n-1)\cdot \left(-(1)/(3)\right)=-(1)/(3)a_(n-1)\\\\\\{\begin{cases}a_1=-3\\a_n=-(1)/(3)a_(n-1)\end{cases}}`