Discrete Mathematics

 

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 x⁴  =  5th number  

 

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

the specific numbers given in the above problem   

 

48 times x⁴  =  243/16    

 

                                                      48x⁴  =  243/16   

 

                                                          x⁴  =  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  

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