Hints and solutions to Look for a pattern #1
What is the sum of the first 4 odd numbers? of the first 5 odd numbers?
of the first 7 odd numbers? of the first 10 odd numbers?
of the first 2356 odd numbers?
The first few of these are easy -- 1 + 3 + 5 + 7 = 16,
1 + 3 + 5 + 7 + 9 = 25 - and you may begin to notice the pattern
that the sum is always a square number. In fact, it is the square of
the number of odd numbers you add together. So the sum of the
first 7 odd numbers is 72 = 49, and the sum of the first
10 odd numbers is 100. Using a calculator or long multiplication, you
can find that the sum of the first 2356 odd numbers is 23562
The figure on the problem page shows that each odd number adds an
additional row and column to the square. And the area of the square,
the sum of the first n odd numbers.