CAT Exam 2021 Slot 2 Solved Paper

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Question : 57 of 66

Marks: +1, -0

For a sequence of real numbers

\x_1,\x_2 ........\x_n

, If

\x_1 - \x_2 = \x_3- ..... + (-1)^{\n + 1} \x_\n = \n^2 +2\n

for all natural numbers n, thenthe sum

\x49 + \x50

equals

200
2
-200
-2

Solution:

Now as per the given series :
we get

x_1 = 1+ 2 = 3

Now

x_1 - x_2 = 8

so

x_2 = -5

Now

x_1 - x_2 + x_3 = 15

so

x_3 = 7

so we get

(x_n = (-1)^{n+1} (2n + 1)

so

x_49 = 99

&

x_50 = -101

Therefore

x_49 + x_50 = -2

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