CAT 2020 Slot 3 QA Question & Solution

AlgebraMedium

Question

If $x_1=-1$ and $x_m=x_{m+1}+(m+1)$ for every positive integer m, then $X_{100}$ equals

Options

-5050

-5151

-5051

-5150

Solution

$x_1=-1$

$x_1=x_2+2$ => $x_2=x_1-2$ = -3

Similarly,

$x_3=x_1-5=-6$

$x_4=-10$

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The series is -1, -3, -6, -10, -15......

When the differences are in AP, then the nth term is $-\frac{n\left(n+1\right)}{2}$

$x_{100}=-\frac{100\left(100+1\right)}{2}=-5050$