Solve the AP – 4 + (–1) + 2 +...+ x = 437.

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answer is B.

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Detailed Solution

Given, the equation – 4 + (–1) + 2 +...+ x = 437.
The equation is like the sum of the terms in AP.
The sum of the first nth terms of an AP,

S n = n 2 2 a + n − 1 d

.
From the equation,

S n = 437, a = − 4

d = − 1 + 4 = 3

437 = n 2 2 − 4 + n − 1 3 437 = n 2 − 8 + 3 n − 3 874 = 3 n 2 − 11 n 3 n 2 − 11 n − 874 = 0

By solving the equation,

3 n 2 − 57 n + 46 n − 874 = 0 3 n n − 19 + 46 n − 19 = 0 3 n + 46 n − 19 = 0 n = 19, − 463

As, n can be a positive integer only and so, we will ignore the negative one.
Now, to find the value of last term,

a n = a + n − 1 d

a n = − 4 + 19 − 1 3 a n = − 4 + 54 a n = 50

The last term of the series is 50.
Therefore, the correct option is 2.

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