#1**+1 **

I don't know if this is the classroom approved method.

A geometric series is formed by multiplying a term by a number to find the next term.

So, if we call that multiplyer number x, then a series would look like this.

1st number times x = 2nd number

2nd number times x = 3rd number

3rd number times x = 4th number

4th number times x = 5th number

By this we can see that 1st number times x^{4} = 5th number

Now that we have a principle established, let's substitute

the specific numbers given in the above problem

48 times x^{4} = 243/16

48x^{4} = 243/16

x^{4} = 243/(16)(48)

x = (243/768)^{1/4}

Using my scientific calculator

to take the fourth root x = 0**.**75

The series is 48, **36**, **27**, **20.25**, 15**.**1875

Note that 15**.**1875 is the same as 243/16

_{.}

Bosco Feb 6, 2024

#1**+1 **

Best Answer

I don't know if this is the classroom approved method.

A geometric series is formed by multiplying a term by a number to find the next term.

So, if we call that multiplyer number x, then a series would look like this.

1st number times x = 2nd number

2nd number times x = 3rd number

3rd number times x = 4th number

4th number times x = 5th number

By this we can see that 1st number times x^{4} = 5th number

Now that we have a principle established, let's substitute

the specific numbers given in the above problem

48 times x^{4} = 243/16

48x^{4} = 243/16

x^{4} = 243/(16)(48)

x = (243/768)^{1/4}

Using my scientific calculator

to take the fourth root x = 0**.**75

The series is 48, **36**, **27**, **20.25**, 15**.**1875

Note that 15**.**1875 is the same as 243/16

_{.}

Bosco Feb 6, 2024