Question

The explicit formula for the geometric sequence -1/9, 1/3, -1, 3, -9, ... is -1/9(-3)^x-1 . What is the common ratio and recursive formula for this sequence

Answer 1

−3; f(x + 1) = −3(f(x))

The answer is B.

Explanation:

Answer 2

• r=3
• 
  `\left\{\begin{array}{ccc}a_1=-(1)/(9)\\a_n=-3a_(n-1)\end{array}\right`

Explanation:

Given the sequence

`-1/9, 1/3, -1, 3, -9, ...`

The common ratio is determined by the division of term by the previous term.

Common Ratio,
`r=(1/3)/(-1/9) =(-1)/(1/3) =(3)/(-1)=-3`

A recursive formula is a formula that defines each term of a sequence using preceding term(s).

For the given sequence, the recursive formula is:

`\left\{\begin{array}{ccc}a_1=-(1)/(9)\\a_n=-3a_(n-1)\end{array}\right`