The diagram shows that 1 + 3 + 5 + 7 = 16.
Q1.) What is the sum of the first 30 odd numbers?
Ans.) In this case, there are 30 odd numbers from 1 to 59.
Using the formula:
30 square which equals to 900.
So, the sum of the numbers is 900.
Q2.) What is the sum of the first 60 odd numbers?
Ans.) As same as before we have to use the same method,
We have 60 odd numbers so using the same formula:
60 square which equals to 3600.
So, the sum of numbers is 3600.
Q3.) Can you describe a method for working these out quickly?
Ans.) Yes, the method is, that the number of numbers for example I took the
first 25 odd numbers then the square of 25 will give out the answer.
Q4.) Can you make 3249 by adding odd numbers in this way?
Ans.) Yes, We have to find out if 3249 is a square number and it is, which is
57, so we can make 3249 by adding odd numbers by this way.
Q5.) What is the value of:
a.) 1+3+...+149+151+153? 5929
b.) 83+81+...+5+3+1? 1762
c.) 51+53+55+...+149+151+153? 5304
d.) 2+4+...+150+152+154? 6006
e.) 2+6+...+298+302+306? 11818
Explain how you worked these out.
Ans.) I worked out the number which are odd by the formula for the other answers but for this one I added then all, as I a sixth grader can solve them.