a) if the sequence is arithmetic, then 

    

     
          
                       <-- so common difference = 4
                
                

first term = x+3 =  =  = 
second term =  =  = 
As a check,
second term = x+7 =  =  = 
third term =  =  = 
As a check,
third term = 4x-2 =  = = 
fourth term =  =  = 


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b) if the sequence is geometric, then 

    

            

        
              
        

        

        

        

Two solutions:
       
    , 

      ,    

                    

Using x=5

first term = x+3 =  = 
second term = x+7 =  = 
common ratio =  =  = 
third term =  = 
As a check,
third term = 4x-2 =  =  = 
fourth term =  = 

Using x=

first term = x+3 =  =  = 
second term = x+7 =  =  = 
common ratio =  =  = 
third term =  = 
As a check,
third term = 4x-2 =  = = 
fourth term =  = 

Edwin