Question

(5)/(9,) (5)/(3,) 5,15,45 are these numbers a sequence of geometric numbers

Answer 1

It is a sequence of geometric numbers.

Explanation:

A sequence or series of numbers where each term after the first term is found by multiplying it with a fixed or certain number is called a geometric sequence or geometric progression.

We can check whether the given series is geometric or not by dividing each term by its previous term to see if their common ratio is the same.

`(45)/(15)=3`

`(15)/(5) =3`

`(5)/((5)/(3) ) =3`

`((5)/(3) )/((5)/(9) ) =3`

Since the common ratio is the same, therefore it is a sequence of geometric numbers.

Answer 2

It is a geometric sequence.

Explanation:

We have given the sequence.

We have to find that is it a sequence of geometric numbers or not.

As we know that:

A geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

So, we have to check that whether it is geometric or not by dividing each term by its previous term .

45/15 = 3

15/5 = 3

5/(5/3) = 3

It is clear that a common ratio is same so, it is a geometric sequence.