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## 'Picturing Square Numbers' printed from http://nrich.maths.org/

The sum of consecutive odd numbers can be represented as square arrays.

The diagram shows that 1 + 3 + 5 + 7 = 16.

What is the sum of the first $30$ odd numbers?

What is the sum of the first $60$ odd numbers?

Have you a method for working this out quickly?

Can you make $3249$ by adding odd numbers in this way?

What is the sum of $1 + 3 + ... + 149 + 151 + 153$?

What is the value of $83 + 81+ ... + 5 + 3 + 1$?

What is the value of $51 + 53 + 55 + ... + 149 + 151 + 153$?

What is the sum of $2 + 4 + ... + 150 + 152 + 154$?

What is the sum of $2 + 6+ ... + 298+ 302+ 306$?

Explain how you worked these out.