then what is the value of x?

this question is from my SAT study guide. Its difficulty is hard.

Thanks so much!

- Apr 26th 2008, 05:59 PMPotterpieIf the sum of the consecutive integers from -22 to x, inclusive, is 72
then what is the value of x?

this question is from my SAT study guide. Its difficulty is hard.

Thanks so much!

- Apr 26th 2008, 06:05 PMicemanfan
- Apr 26th 2008, 06:06 PMTKHunny
-22 + -21 + -20 + ... + x = 72

Obviously, x > 0, otherwise you'll never get to 72 after starting negative.

Your task is to express that string of values more conveniently.

You should have some familiarity with the "Arithmetic Sequence"

-22 = -22

-21 = -22 + 1

-20 = -22 + 1(2)

-19 = -22 + 1(3)

...

x = -22 + 1(22+x)

Where does that leave us? - Apr 26th 2008, 06:06 PMPotterpie
Wouldn't it be 44?

@Hunny: I haven't learned arithmetic sequence yet because I haven't finished algebra II. unless I was supposed to learn it by now.

But your last equation, x=-22+1(22+x), simplified, just leaves me with x=x. - Apr 26th 2008, 06:11 PMicemanfan
- Apr 26th 2008, 06:11 PMGusbob
Edit: see the post above, if you haven't learnt arithmetic series the above way is the best.

- Apr 26th 2008, 06:13 PMicemanfan
- Apr 26th 2008, 06:16 PMGusbob
- Apr 26th 2008, 06:17 PMPotterpie
Okay, iceman's post made sense but I'm pretty sure we're not supposed to go through and add every single one. the SAT is timed.

Gusbob, that equation works once you change 48 to 49 (because I know the answer is 25, I just don't know how to get it), but where did you come up with that?

and hunny's equation just left me with x=x. You distribute the 1 into the parenthesis and then you end up with x=-22+22+x. - Apr 26th 2008, 06:19 PMGusbob
Iceman's post is suggesting that the sum of -22 to 22 is 0

(-22 + 22) + (-21 + 21)+ ...+ (-1 + 1) + 0 = 0 - Apr 26th 2008, 06:20 PMicemanfan
- Apr 26th 2008, 06:23 PMPotterpie
I just calculated it. If you add up -22+-21, all the way to -1, the sum is not 0. It's -253 because you add consecutive negative integers.

I just have to figure out which number, x, to go up to to make the sum 72 instead of -253. <-- or wait, nvm. I don't know. Is that right? All I know is x=25. D: - Apr 26th 2008, 06:27 PMicemanfan
- Apr 26th 2008, 06:29 PMPotterpie
Okay, true. Right.

Then where do I go from that to get x=25? - Apr 26th 2008, 06:42 PMicemanfan