SOLUTION: How do I find the pattern to the sequence? 1,4,9,1,6,2,5,3,6,4,9,6,4 _,_,_,_ I would also like and explanation how to get the answer so I can explain it to my daughter.

Question 97340: How do I find the pattern to the sequence?
1,4,9,1,6,2,5,3,6,4,9,6,4 _,_,_,_
I would also like and explanation how to get the answer so I can explain it to my daughter.
Found 3 solutions by stanbon, jim_thompson5910, mathslover:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
1,4,9,1,6,2,5,3,6,4,9,6,4,8,1, _,_,_,_
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You have 1^2=1, 2^2=4, 3^2=9, 4^2=16,...8^2=64,9^2=81
==================
Cheers,
Stan H.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Notice the first three terms

1,4,9

This looks like it might be the sequence of perfect squares. If you look at the next number you'll see 1. But if you look at the next two numbers as one number, you'll see 16. Once again if you look at the next pair as one number you get 25. If you keep doing this you get the sequence:

1,4,9,16,25,36,49,64,...

So that means the next two numbers are 81 and 100. These break down into

8,1,1,0,0

So the entire sequence then becomes

1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,1,0,0

But since the problem only asks for 4 numbers, we must drop the last zero. So the sequence is

1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,1,0
Answer by mathslover(157)   (Show Source): You can put this solution on YOUR website!
1,4,9,1,6,2,5,3,6,4,9,6,4 _,_,_,_
observe the first number it's 1^2 =1
the second number is 2^2 =4
the third number is 3^2 = 9
the 4th and 5th number represents the square of 4 ie 4^2 = 1,6
the 6th and 7th number represents the sqaure of 5 ie 5^2 = 2,5
and so on ...
the first 2 blanks represent the square of 9 which is 8,1
the next 2 blanks should represent the square of 10 which is 1, 00

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