Question

Solve the equation:
(-4) + (-1) + 2 + ------- + x = 437
Pls give steps of solution too....

Answer 1

What do all the dashes mean?

Answer 2

\[(-4)+(-1)+2+...+x=437\]?
continuation of the pattern, whatever it is?
I don't get it.

Answer 3

the dashes mean that there are other numbers in between 2 and x

Answer 4

this loook like an A P

Answer 5

well the pattern most obvious is what jimmyrep says: +3

Answer 6

sum = 437

Answer 7

It is an A.P. but somehow today the bell is not ringing for me!!!

Answer 8

Here u r not given the terms themselves......

Answer 9

437 = n/2 [-8 + (n-1)3]

Answer 10

This looks like the sum of an arithmetic series: http://regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

Answer 11

50

Answer 12

that is, x = 50

Answer 13

Yeah, but ow do you "show" it? I used my calculator.

Answer 14

you have
\[\sum_{k=0}^n3k-4=437\] there is a snappy way to sum an arithmetic series, but i always forget it. in any case you are solving for n

Answer 15

yea solve for n then x = nth term

Answer 16

being a bonehead and forgetting the simple way, i usually work with
\[\sum_{k=1}^nk =\frac{n(n+1)}{2}\] and work from there

Answer 17

lol - you're no bonehead!

Answer 18

i think jimmyrep has it, the summation formula i mean

Answer 19

i can work out the steps i took if you like. since i only remember that
\[\sum_{k=1}^n k =\frac{n(n+1)}{2}\] i wrote the sum as
\[\sum_{k=1}^n -7+3k=-7\sum_{k=1}^n1+3\sum_{k=1}^n k\]
\[=-7n+\frac{3n(n-1)}{2}=437\] solve for n get
\[n=19\] replace k by 19 in
\[-7+3k\] get x =50

Answer 20

anyway guys i'm signing - i'm just on my fourth beer and thinking is getting too hard
HAPPY NEW YEAR guys

Answer 21

happy new year all, see you in 2012

Answer 22

Hey guys, HAPPY NEW YEAR to u ALL !!!!

Answer 23

Pls check if my working below is correct...

Answer 24

looks like i missed a cool problem

Answer 25

No, you get to check Harkirat's work still :)

Answer 26

The formula for the sum is
Sn = n/2[2a+(n-1)d]
here Sn= 437
a = -4
d = 3
so
437 = n/2[2(-4) + (n-1)(3)]
874 = n[-8 + 3n -3]
which gives
3n^2 - 11n - 874 = 0
solving which we get n = 19 or n = -46/3
since term no cannot be negative, so n = 19

Answer 27

so x is the 19th term
using An = a + (n-1)d
x = (-4) + (19-1)(3)
x = -4 + 54
x = 50

Answer 28

look right to me, but I had to look up that formula.

Answer 29

(-4+0(3))+(-4+1(3))+(-4+2(3))+....+(-4+n(3))=437 (so this means x=-4+3n)
\[-4(n+1)+3\sum_{i=0}^{n}i=437\]
\[-4n-4+3(0)+3 \sum_{i=1}^{n}i=437\]
\[-4n+3 \cdot \frac{n(n+1)}{2}=441\]
\[-8n+3n(n+1)=882\]
\[-8n+3n^2+3n=882\]
\[3n^2-5n-882=0\]
\[n=\frac{5 \pm \sqrt{25-4(3)(-882)}}{2(3)}=\frac{5 \pm 103}{6}=\frac{108}{6} \text{ or } \frac{-98}{6}\]
We don't want the negative value (also that would give us an irrational answer and we want n to be an integer)
so we have
\[n=\frac{108}{6}=18\]
=> x=-4+3n=-4+3(18)=50
This is the way I would have done it.
This is a nice problem! :)

Answer 30

I forgot about making it -4(n+1) outside the sum sign when you start from zero, so I kept messing it up starting doing -4n. I'm a series rookie.

Answer 31

Well I like my way because I understand it best! :)
I like how Satellite and Harkirat did it different ways.

Answer 32

Thanks to all!!! Actually I had to get the solution with the formulas I used. My students have not been taught the summation method/formula yet......

@TuringTest... Don,t worry, we all make mistakes. I was also making a small mistake in my calculation due to which I was getting both values of n as negative and hence was foxed. However, when I did it here, I did it right and got the positive value of n....and then it was easy to get the final answer☺

Answer 33

Where did you get this problem?

Answer 34

I have a problem to give to my students now. :)

Answer 35

Can't wait!

Answer 36

I take private tuition and one of the students just gave it to me over phone as he has to submit the assignment tomorrow......

Answer 37

You do tutoring over the phone?

Answer 38

*I give private tuition....

Answer 39

private tutoring?

Answer 40

Sometimes....when they forget to ask when they come to me for tuition...
I even teach a kid in USA via the internet....

Answer 41

Private tutoring means that besides going to school, the kids come to me for one-on-one lessons where I clear all their doubts and explain concepts as per their standard level...

Answer 42

Cool! :)

Answer 43

Are you also a teacher??☺

Answer 44

Yes I teach.

Answer 45

I am from India and you are from??

Answer 46

United States. You know I remember you from awhile back. Its been awhile since I seen you. Do you remember me?

Answer 47

Of course, I do!!!!

Answer 48

Actually I have got real busy these last few months, even my nights are taken by my US student plus I got bored with solving the same type of problems again and again and do not come to openstudy so much nowadays....☻

Answer 49

I think you always had some cool questions. I sort remember something from you a long time ago, but I can't remember it exactly.

Answer 50

I guess they r interesting because I myself find them tough !!! LOL !!!!
However, the moment I put them out here, somehow the solution comes running to my mind....like magic....

Answer 51

lol

Answer 52

Hey myininaya, I got a favour to ask....

Answer 53

oh I'm sorry what?