cat 2021 Question 20

Question

For a sequence of real numbers $x_1$, $x_2$, ..., $x_n$, if $x_1$ - $x_2$ + $x_3$ - ... + $(-1)^n + 1$$x_n$ = $n^2$ + 2n for all natural numbers n, then the sum $x_49$ + $x_50$ equals

Accepted Answer

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 $x_{49} = 99$ and $x_{50} = -101$

Therefore, $x_{49} + x_{50} = -2$

Question 20.

Question Explanation