SOLUTION: I have tried for a long time to figure out, what the following numbers are: 2 5 19 x y Anyone who can give me a hint? Tine Denmark

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Question 836844: I have tried for a long time to figure out, what the following numbers are:
2 5 19 x y
Anyone who can give me a hint?
Tine
Denmark
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
I have tried for a long time to figure out, what the following numbers are:
2 5 19 x y
Anyone who can give me a hint?
---------------------------
As with a lot of these problems, more than 1 answer is possible.
---
1 possibility:
The 1st difference (5-2) = 3
The 2nd is 14, an increase of 11.
--> 3rd difference = 14 + 11 = 25, etc
--> 2 5 19 44 80
======================
Another is:
5 = 3*2 - 1
19 = 5*4 - 1
--> x = 19*6 - 1 = 113
--> y = 113*8 - 1 = 903
==============================
These problems are useless, and a waste of time.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
t(n) = an² + bn + c

t(1) = a(1)² +b(1) + c =  a +  b + c = 2
t(2) = a(2)² +b(2) + c = 4a + 2b + c = 5
t(3) = a(3)² +b(3) + c = 9a + 3b + c = 19



Solve that system and get a = , b = , c = 

t(n) = an² + bn + c

t(n) =  

t(1) =  = 2

t(2) =  = 5

t(3) =  = 19

t(4) =  = 44 = x

t(5) =  = 80 = y

Edwin
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