1000 PS section 24- Q-8

x[(x+1)]/2 = (11-x)(x+10)/2 +1

=>(x^2+x)/2 =[ (11x+110-x^2-10x)/2 ] +1

=>x^2+x = x+108-x^2

=>2x^2-108=0

=>x^2= 54

=> x=sqrt 54

what mistake i am doing here???

ok i jus did lit like this:
1 2 3 4 5 6 7 8 9 10
I started at wat if x = 5? i could readily see that it couldnt equal to 5 because 6+7+8+9+10 is far more than 1 when subracted by 1+2+3+4+5
I went up to x =6, still it wasnt one more
I went up to x=7, 1+2+3+4+5+6+7 = 28 then 8+9+10=27. this is the answer. x =7

pathaniaus wrote:ok i jus did lit like this:
1 2 3 4 5 6 7 8 9 10
I started at wat if x = 5? i could readily see that it couldnt equal to 5 because 6+7+8+9+10 is far more than 1 when subracted by 1+2+3+4+5
I went up to x =6, still it wasnt one more
I went up to x=7, 1+2+3+4+5+6+7 = 28 then 8+9+10=27. this is the answer. x =7

thanks for the answer..

But is there a way we can make algebraic equation out of it?

Well this can be solved using Arithmetic Progression

Formula for AP is n(a1+an)/2

n = numbers in a sequence

Given the question we can come up with the following equation

n(1+x)/2 = (10-n)((X+1) + 10)/2 +1

We can replace n with x because we have consecutive numbers. Once we solve this we will get the quadratic equation

X^2 +x -56 = 0, the answer is -8, 7. So x is 7

Hope it helps.

Vineet

Well this can be solved using Arithmetic Progression

Formula for AP is n(a1+an)/2

n = numbers in a sequence

Given the question we can come up with the following equation

n(1+x)/2 = (10-n)((X+1) + 10)/2 +1

We can replace n with x because we have consecutive numbers. Once we solve this we will get the quadratic equation

X^2 +x -56 = 0, the answer is -8, 7. So x is 7

Hope it helps.

Vineet

Well this can be solved using Arithmetic Progression

Formula for AP is n(a1+an)/2

n = numbers in a sequence

Given the question we can come up with the following equation

n(1+x)/2 = (10-n)((X+1) + 10)/2 +1

We can replace n with x because we have consecutive numbers. Once we solve this we will get the quadratic equation

X^2 +x -56 = 0, the answer is -8, 7. So x is 7

Hope it helps.

Vineet

Apologies for the same post 3 times, I had a problem with my browser.