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

Question

Accepted Answer

-5050. x 1 = − 1 x_1=-1 x 1 ​ = − 1 x 1 = x 2 + 2 x_1=x_2+2 x 1 ​ = x 2 ​ + 2 => x 2 = x 1 − 2 x_2=x_1-2 x 2 ​ = x 1 ​ − 2 = -3 Similarly, x 3 = x 1 − 5 = − 6 x_3=x_1-5=-6 x 3 ​ = x 1 ​ − 5 = − 6 x 4 = − 10 x_4=-10 x 4 ​ = − 10 . . The series is -1, -3, -6, -10, -15...... When the differences are in AP,

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

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

If x1=−1x_1=-1x1​=−1 and xm=xm+1+(m+1)x_m=x_{m+1}+(m+1)xm​=xm+1​+(m+1) for every positive integer m, then X100X_{100}X100​ equals

If x1=−1x_1=-1x1​=−1 and xm=xm+1+(m+1)x_m=x_{m+1}+(m+1)xm​=xm+1​+(m+1) for every positive integer m, then X100X_{100}X100​ equals

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

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