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Quantitative Aptitude Question on Sequence and Series

For a sequence of real numbers x1,x2,...,xn,x_1, x_2, ..., x_n, if x1−x2+x3−...+(−1)n+1xn=n2+2nx_1 - x_2 + x_3 - ... + (-1)^{n + 1}x_n =n^2 + 2n for all natural numbers n, then the sum x49+x50x_{49} + x_{50} equals

A

2

B

-2

C

200

D

-200

Answer

-2

Explanation

Solution

From the given series we have:x1=1+2=3x_1=1+2=3
Now x1−x2=8x_1-x_2=8
⇒x=−5⇒ x=-5

We have : x1−x2+x3=15x_1-x_2+x_3=15
⇒x3=7⇒ x_3=7
So,we have: xn=(−1)n+1(2n+1)x_n=(-1)^{n+1}(2n+1)
⇒x49=99⇒ x_{49}=99
⇒x50=−101⇒ x_{50}=-101
∴x49+x50=−2∴ x_{49}+x_{50}=-2