Math help?

Question

Today in math we were asked this question

What is the sum of the first 300 odd numbers?

He said that there is an easier way to find the answer besides having to add it one by one on the calculator. Does anyone know how to get the answer?

I'm not here so you guys can do my homework, I seriously don't know how I could do this.

Please help

Daaaang Mcfake, That sounded like another language. haha thxs

Answer 1

ITS SOMETHING LIKE:
299 (LAST ONE) + 1 (FIRST ONE) x 150 (THE # OF ODD #'S) / 2 (TAKES 2 TO MAKE A PAIR)
SO I THINK IT'S 300 x 150 / 2
=22,500?
OOPS THOUGHT IT SAID FIRST ODD NUMBERS UP TO 300
(599+1)(300)/2
=90,000

Answer 2

"Odd numbers" form an arithmetic series, with a constant difference of 2 between each adjacent term in the series.

The sum of an arithmetic series is the average of the first and last term, times the number of terms. We already know the first term (1), the number of terms (300), and we just need to find the last one (300th odd number) to do the calculation.

The first odd number is 1, the second is 3, the third is 5, etc., so the Nth is 2*N - 1. (2*1-1 = 1, 2*2-1 = 3, ...).

The 300th odd number is therefore (2*300 - 1), which is 599. Now, having all three numbers, we can calculate the answer:

sum = terms * (firstTerm + lastTerm) / 2
sum = 300 * (599 + 1)/2
sum = 300 * 300
sum = 90,000