# Next Number in the Sequence

What is the next number in the sequence below:

1          4          9          7          7          9         4          1          ?

### 3 guesses to Next Number in the Sequence

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• Margot

Because it’s late in the day, and I can’t see any hidden trick in this, I’d say 1.

• Matt

I believe these are derived by finding the sums of the digits of the first 8 numbers squared.
1 x 1 = 1 (Sum: 1)
2 x 2 = 4 (Sum: 4)
3 x 3 = 9 (Sum: 9)
4 x 4 = 16 (Sum: 1 + 6 = 7)
5 x 5 = 25 (Sum: 2 + 5 = 7)
6 x 6 = 36 (Sum: 3 + 6 = 9)
7 x 7 = 49 (Sum: 4 + 9 = 13 -> Sum: 1 + 3 = 4)
8 x 8 = 64 (Sum: 6 + 4 = 10 -> Sum: 1 + 0 = 1)

Thus, the answer could be 9.
9 x 9 = 81 (Sum: 8 + 1 = 9)

I think this is referred to as finding the digital root.

• Matt, you are today’s winner!
The sequence reflects a single-digit sum of the digits of the squares of the first 9 counting numbers, obtained by adding the two digits together until a single digit results…… 1 squared = 1 2 squared = 4 3 squared = 9 4 squared = 16 ( 1 + 6 = 7 ) 5 squared = 25 ( 2 + 5 = 7 ) 6 squared = 36 ( 3 + 6 = 9 ) 7 squared = 49 ( 4 + 9 = 13 ) ( 1 + 3 = 4 ) 8 squared = 64 ( 6 + 4 = 10 ) ( 1 + 0 = 1 ) 9 squared = 81 ( 8 + 1 = 9 ).