Solve the question: (-4) + (-1) + 2+5 + ... + x=437

The sequence is an arithmetic sequence with

a₁ = - 4

d = a₂ - a₁

d = - 1 - (-4)

d = - 1 + 4

d = 3

an = x

Sn = 437

General formula in arithmetic sequence

Formula to find nth term

an = a₁ + d (n - 1)

Formula to find sum of sequence (sn)

Sn = n/2 (a₁ + an)

We have to make an equation system based on the problem

plug the numbers into the formula

First equation

an = a₁ + d (n - 1)

x = - 4 + 3 (n - 1)

x = - 4 + 3n - 3

x = 3n - 7

Second equation

Sn = n/2 (a₁ + an)

n/2 (a₁ + an) = 437

n/2 (-4 + x) = 437

n (x - 4) = 874

xn - 4n = 874

Solve the equation system by subtitution method

Subtitute x with 3n - 7 in the second equation

xn - 4n = 874

(3n - 7) n - 4n = 874

3n² - 7n - 4n = 874

3n² - 11n - 874 = 0

(3n + 46) (n - 19) = 0

n = - 46/3 or n = 19

Because the number of terms shouldn't be negative, - 46/3 isn't required, so the value of n is 19.

Solve for x, back to the first equatin

x = 3n - 7

x = 3 (19) - 7

x = 57 - 7

x = 50

The solution is 50