SOLUTION: what comes after 3.5,13,41.5,127, , , ,

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Question 956201: what comes after 3.5,13,41.5,127, , , ,
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
We try to find a multiplier, m, and an adder, a

 3.5m+a =  13
  13m+a =  41.5
41.5m+a = 127

Removing the decimals by multiplying each through by 2

  7m+2a = 26
 26m+2a = 83
 83m+2a = 254

Solve the first for 2a

    2a = 26-7m

Substitute in the second

 26m+26-7m = 83
    19m+26 = 83
       19m = 57
         m = 3

Substitute in 

   2a = 26-7m
   2a = 26-7(3)
   2a = 26-21
   2a = 5
    a = 2.5


See if those values satisfy

       83m+2a = 254
 83(3)+2(2.5) = 254
      249 + 5 = 254
          254 = 254

Yes they do!

So substituting in

 3.5m+a =  13
  13m+a =  41.5
41.5m+a = 127

  3.5(3)+2.5 =  10.5+2.5 = 13
   13(3)+2.5 =    39+2.5 = 41.5
 41.5(3)+2.5 = 124.5+2.5 = 127  
    
Continuing the pattern:

   127(3)+2.5 =    381+2.5 =  383.5
 383.5(3)+2.5 = 1150.5+2.5 = 1153
  1153(3)+2.5 =   3459+2.5 = 3461.5      

Edwin