Question

solve for x : -4 + - 1 + 2 +....+x=43726

Answer 1

So, it is an A. P. with the first term -4 & common difference is

$- 1 - ( - 4) = 3$

Let, The term X is the n+1 th term of this A. P.

This means the A. P. has n+1 terms in total.

Therefore, using the term formula & summation formula we get...

$x = ( - 4) + n \times 3 \\ and \: 43726 = \frac{n + 1}{2} ( - 4 + x)$

If we put the value of x from the first equation in the second one we get...

$43726 = \frac{n + 1}{2} ( - 4 + ( - 4 + 3n)) \\ or \: 43726 \times 2 = (n + 1)(3n - 8)$

Or,

$3 {n}^{2} - 5n - 8 = 87452$

Now You can solve this equation...

or can replace n from the second equation using x from the first one..

Go ahead