If x₁ = - 1 and xm = xm+1 + (m + 1) for every positive integer m, then x100 equals
Explanation:
Given, xm = xm+1 + (m + 1)
⇒ xm+1 = xm - (m + 1)
Put m = 1 ⇒ x2 = -1 – 2 Put m = 2 ⇒ x3 = -1 - 2 – 3 Put m = 3 ⇒ x4 = - 1 – 2 - 3 – 4
And so on.
∴ x100 = - 1 – 2 – 3 -4 … - 100
⇒ x100 = - (100 × 101)/2 = - 5050
Hence, option (c).
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