CAT 2020 Exam Shift 3 Solved Paper

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Question : 55 of 76

Marks: +1, -0

If

x_{1}=-1

and

x_{m}=x_{m+1}+(m+1)

for every positive integer m, then

x_{100}

equals

$-5151$
$-5150$
$-5051$
$-5050$

Solution:

x_{w}+1=x_{w}-(m+1)

x_{2}=x_{1}-2=-1-2=-3

x_{3}=x_{2}-3=-1-2-3=-6

Similarly,

x_{n}=-(1+2+3+. . .+n)=-\;{n(n+1)}/{2}

Hence

x_{100}=-\;{100(101)}/{2}=-5050

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