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Odd numbers added in order

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Add every odd integer from $1$ up to $39$ inclusive.

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Hint

Each new odd number extends a square by one layer.

Solution

The odd numbers $1, 3, 5, \dots, 39$ number $20$ , since the $n$ -th odd number is $2 n - 1$ and $2 \times 20 - 1 = 39$ .
The sum of the first $n$ odd numbers is $n^{2}$ .
So the sum is $2 0^{2}$ .
The sum is $400$ .

Answer: $400$