Question

What is the common ratio of the sequence xºy?, -exy, 2x2y....?

Answer 1

Given the sequence:

`(1)/(64)x^9y^7,-(5)/(32)x^6y^8,(25)/(16)x^3y^9,\ldots\ldots..`

the common ratio is the ratio between every two adjacent terms

So, we will find the ratio between the second term and term and the first term as follows:

`-(5)/(32)x^6y^8/(1)/(64)x^9y^7`

Simplifying the division process:

`=-(5)/(32)\cdot(64)/(1)\cdot(x^6)/(x^9)\cdot(y^8)/(y^7)=-10\cdot(1)/(x^3)\cdot y=-(10y)/(x^3)`

So, the common ratio =

`-(10y)/(x^3)`