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प्रश्न
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
उत्तर
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: Sn = 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
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