maths Maths Puzzle

Ms. Arroyo asked the class to see if they could find the sum of the first 50 odd numbers. As everyone settled down to their addition, Terry ran to her and said, "The sum is 2,500." Ms. Arroyo thought, "Lucky guess," and gave him the task of finding the sum of the first 75 odd numbers. Within 20 seconds, Terry was back with the correct answer of 5,625.

How does Terry find the sum so quickly?

Read Solution (Total 3)

she squared the no.but the answer is wrong
11 years agoHelpfull: Yes(1) No(0)

first odd no=1
75 th odd no would be 2*74+1=149
(nth odd term is=2*(n-1)+1)
sum=n/2(a+l);
n= no of terms
a=1st term
l=last term
therefore
sum=75/2*(149+1)=5625
11 years agoHelpfull: Yes(0) No(0)
first series is 1,3,5.....99
so sum =(a+l)n/2
so sum= (1+99)*50/2=2500
second =1,3,...149
sum=(1+149)*75/2
=75*75
=5625
10 years agoHelpfull: Yes(0) No(0)

maths Other Question

Some people believe that January 1, 2000 is the first day of the 21st century. Other people believe that the honor belongs to January 1, 2001. But everyone should agree that January 1, 2002 is the first "sum-day" of the new century- when you write out that date in standard notation, it becomes 01/01/02, and 1+1=2. More generally, a sum-day is a date in which the day and month add up to the year. With that in mind:

A) What is the last sum-day of the 21st century?

B) How many sum-days are there in the 21st century?
You have a piece of paper, 10cm by 10cm. Area = 100cm^2. For some reason, you need a square piece of paper with an area of 50cm^2. Using the paper you have, what's an easy way of getting the new square?