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
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
