SOLUTION: Use inductive reasoning to find the next two terms in each sequence 360,180,120,90,____,____ 1,5,14,30,55,___,_____

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Question 803100: Use inductive reasoning to find the next two terms in each sequence
360,180,120,90,____,____
1,5,14,30,55,___,_____

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
360,180,120,90, x , y 

180%2F360 equals to 1%2F2
120%2F180 equals to 2%2F3
90%2F120 equals to 3%2F4
So inductively,
x%2F90 must equal to 4%2F5
 x%2F90%22%22=%22%224%2F5
5x = 360
 x = 72
Also inductively,
y%2Fx or y%2F72 must equal to 5%2F6
      y%2F72%22%22=%22%225%2F6
     6y = 360
      y = 60

360,180,120,90, 72 , 60 .

-------------------------------------

 1,5,14,30,55, x , y 

  5-1 equals to 4, which equals to 2².
 14-5 equals to 9, which equals to 3².
30-14 equals to 16, which equals to 4².
55-30 equals to 25, which equals to 5².

So inductively,
x-55 must equal to 6² or 36
x-55 = 36
   x = 91
 
Also inductively,
y-x or y-91 must equal to 7² or 49
       y-91 = 49
          y = 140

 1,5,14,30,55, 91 , 140 .

Edwin