# Thread: What is the average of the first 30 positive integers?

1. ## What is the average of the first 30 positive integers?

What is the average of the first 30 positive integers?
Hi all, I'm guessing 15 but

How do you figure this problem out, that is:
what is the layout of the math reasoning?
Studying for an exam for Monday... your help is appreciated
thanks

Here's another prob:
A is 1,000(1+2+ ...+100)
B is 2,000(1+2+ ...+100)
B-A would be 1,000(1+2+ ...+100) , right?
Then how can you know without doing the summing, what
1,000(1+2+ ...+100) is?
Is there a "trick" to the number relationships?

One thing, we know that 100+99 is 199 almost 200 so 1,000*200 is 200,000 so the answer would have to be more than that.
is this the only way to "figure " this out? or are there other ways?
ok

2. The sum of the numbers from 1 to n is given by:
$\displaystyle S_n = \frac{n(n+1)}{2}$

3. Originally Posted by eri
What is the average of the first 30 positive integers?
Hi all, I'm guessing 15 but

How do you figure this problem out, that is:
what is the layout of the math reasoning?
the sum of the first n positive integers is $\displaystyle \frac {n(n + 1)}2$

thus, the average of the first 30 positive integers is $\displaystyle \frac 1{30} \cdot \frac {30(30 + 1)}2 = 15.5$

for the second problem your conjecture is correct. to find the actual number, you would use the formula i gave you above

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