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

Answer:

• r=3
• $\left\{\begin{array}{ccc}a_1=-\frac{1}{9}\\a_n=-3a_{n-1}\end{array}\right$

Step-by-step 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, $r=\frac{1/3}{-1/9} =\frac{-1}{1/3} =\frac{3}{-1}=-3$

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:

$\left\{\begin{array}{ccc}a_1=-\frac{1}{9}\\a_n=-3a_{n-1}\end{array}\right$

Answer 2

Answer:

−3; f(x + 1) = −3(f(x))

The answer is B.

Step-by-step explanation: