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$

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

-2. Now as per the given series : we get x 1 = 1 + 2 = 3 x_1=1+2\ =3 x 1 ​ = 1 + 2 = 3 Now x 1 − x 2 = 8 x_1-x_2=\ 8 x 1 ​ − x 2 ​ = 8 so x 2 = − 5 x_2=-5 x 2 ​ = − 5 Now x 1 − x 2 + x 3 = 15 x_1-x_2+x_3\ =\ 15 x 1 ​ − x 2 ​ + x 3 ​ = 15 so x 3 = 7 x_3\ =7 x 3 ​ = 7 so we get x n = ( − 1 ) n + 1 ( 2 n +

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

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

For a sequence of real numbers x1,x2,...xnx_{1},x_{2},...x_{n}x1​,x2​,...xn​, If x1−x2+x3−....+(−1)n+1xn=n2+2nx_{1}-x_{2}+x_{3}-....+(-1)^{n+1}x_{n}=n^{2}+2nx1​−x2​+x3​−....+(−1)n+1xn​=n2+2n for all natural numbers n, then the sum x49+x50x_{49}+x_{50}x49​+x50​ equals

For a sequence of real numbers x1,x2,...xnx_{1},x_{2},...x_{n}x1​,x2​,...xn​, If x1−x2+x3−....+(−1)n+1xn=n2+2nx_{1}-x_{2}+x_{3}-....+(-1)^{n+1}x_{n}=n^{2}+2nx1​−x2​+x3​−....+(−1)n+1xn​=n2+2n for all natural numbers n, then the sum x49+x50x_{49}+x_{50}x49​+x50​ equals

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

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