Question

Solve the equation:

– 4 + (–1) + 2 + 5 + ... + x = 437

Answer 1

Given equation is,

– 4 + (–1) + 2 + 5 + … + x = 437 

Here, –4 – 1 + 2 + 5 + … + x is in A.P.

Then, a = -4, d = -1 + 4 = 3, l = x

Given: S_n = 437

⇒ `"n"/2[2"a" + ("n" - 1)"d"]=437`

⇒ n[-8 + 3n - 3] = 874

⇒ 3n² - 11n - 874 = 0

⇒ 3n² - 57n + 46n - 874 = 0

⇒ 3n(n - 19) + 46(n -19) = 0

⇒ (n - 19) (3n + 46) = 0

⇒ n - 19 = 0, n = 19

⇒ 3n + 46 = 0

n = `-46/3` (Impossible)

Hence, n = 19

So, l = a + (n - 1)d

x = -4 + (19 - 1) 3

= -4 + 18 × 3

= -4 + 54

x = 50