Gauss method: finding the number of terms in A.P

[Simonsky]

Sorry folks, I'm stuck again on another arithmetic progression question:

basically a=4 and d=6 and the sum of the terms is 444. Question asks to find n.

So I used the formula: n/2[ 2a +(n-1)d] = 444 and continued:

n/2(8+6n -6) = 444 then factoring with 2 = n/2X2(4+3n -3) = 444

then: n(1-3n) = 444 followed by: 3n^2 +n = 444 becoming: 3n^2+n - 444 =0

Then I'm stuck because I can't factor it using the 'splitting method' ( two factors of 444 with a difference of 1 doesn't exist).

Any help appreciated ( can't use formula because the 444 would make a square root of a negative number therefore imaginary). I've probably overlooked something obvious, I always do

 

[Deleted member 4993]

Sorry folks, I'm stuck again on another arithmetic progression question:

basically a=4 and d=6 and the sum of the terms is 444. Question asks to find n.

So I used the formula: n/2[ 2a +(n-1)d] = 444 and continued:

n/2(8+6n -6) = 444 then factoring with 2 = n/2X2(4+3n -3) = 444

then: n(1-3n) = 444 (?) followed by: 3n^2 +n = 444 becoming: 3n^2+n - 444 =0

Then I'm stuck because I can't factor it using the 'splitting method' ( two factors of 444 with a difference of 1 doesn't exist).

Any help appreciated ( can't use formula because the 444 would make a square root of a negative number therefore imaginary). I've probably overlooked something obvious, I always do

n/2 * [ 2*a +(n-1)*d] = 444

n/2 * [ 2*4 +(n-1)*6] = 444

n/2 * [ 8 + 6*n - 6] = 444

n * [ 1 + 3*n] = 444

3n² + n - 444 = 0

Did you learn to use "quadratic formula"? I do not understand your statement "can't use formula because the 444 would make a square root of a negative number therefore imaginary"

By the way the solution of the above equation is n = 12 & -12.3333 (or 12 1/3)

 

[Dr.Peterson]

Sorry folks, I'm stuck again on another arithmetic progression question:

basically a=4 and d=6 and the sum of the terms is 444. Question asks to find n.

So I used the formula: n/2[ 2a +(n-1)d] = 444 and continued:

n/2(8+6n -6) = 444 then factoring with 2 = n/2X2(4+3n -3) = 444

then: n(1-3n) = 444 followed by: 3n^2 +n = 444 becoming: 3n^2+n - 444 =0

Then I'm stuck because I can't factor it using the 'splitting method' ( two factors of 444 with a difference of 1 doesn't exist).

Any help appreciated ( can't use formula because the 444 would make a square root of a negative number therefore imaginary). I've probably overlooked something obvious, I always do

You CAN always use the quadratic formula; if it gives an imaginary answer, that just tells you that there is NO real solution -- by ANY method.

But I get an integer solution, not imaginary. Try the calculation again, and if you still don't get it, show the details of your calculation from the quadratic formula.

Also, the method I know of for factoring uses two factors of ac = 3*444, not of 444 itself.

 

[Simonsky]

Many thanks

Thanks to both of you for the help -I'd forgotten to multiply the 444 X 3

I find I often overlook obvious things-oh dear!

Many thanks, again