Solve the equation: - 4 + (-1) + 2 +...+ x = 437
Solution:
Given, the series is -4, -1, 2, ……, x
We have to find the value of x.
Here, first term, a = -4
Last term, l = x
Sum of the series, S = 437
Common difference, d = -1 - (-4) = -1 + 4 = 3
The nth term of the series in AP is given by
aₙ = a + (n - 1)d
So, x = -4 + (n - 1)3
x = -4 + 3n -3
x = 3n - 7
3n = x + 7
n = (x+7)/3
If l is the last term of an AP, then the sum of the terms is given by
S = [n/2][a+l]
So, S = [(x+7)/6][(-4+x)]
437 = [(x+7)(x-4)]/6
437(6) = (x² + 7x - 4x - 28)
x² + 3x - 28 = 2622
x² + 3x - 2650 = 0
On factoring,
x² + 53x - 50x - 2650 = 0
x(x + 53) - 50(x + 53) = 0
(x - 50)(x + 53) = 0
Now, x + 53 = 0
x = -53
Also, x - 50 = 0
x = 50
Since a negative integer is not possible, x = -53 is neglected.
Therefore, the value of x is 50.
✦ Try This: Solve the equation: - 4 + (-1) + 2 +...+ x = 387
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.4 Problem 8
Solve the equation: - 4 + (-1) + 2 +...+ x = 437
Summary:
On solving the equation - 4 + (-1) + 2 +...+ x = 437, the value of x is 50
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