Question

Natalia is writing a recursive formula to represent the sequence.

8, 12, 18, 27, ..
What value should she use as the common ratio in the formula?

Answer 1

1.5

Explanation:

The common ratio if there exists one can be found by choosing a term and dividing by its previous term

So does 12/8=18/12=27/18? Put each into the calculator. If they are equal fractions then this sequence is geometric and has a commom ratio.

Each of the fractions are equal to 1.5.

Therefore the commom ratio is 1.5.

Answer 2

`r=(3)/(2)`

Explanation:

Since Natalia is about to write a Recursive Formula, i.e. a Formula that write this sequence in terms of a function. She'll need the common ratio. To find this, since it is clearly not an Arithmetic Sequence, but a Geometric one let's divide one consequente term over the antecedent term.

`(12)/(8)=(18)/(12)=(27)/(18)=(3)/(2)`

Recursive formula:

`f(n)=f(n-1)*(3)/(2)`