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Aliya Baxter
Mathematics
8 January, 02:30
Solve the question: (-4) + (-1) + 2+5 + ... + x=437
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Maximilian Archer
8 January, 02:51
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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
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