If x 1- x 2- x 3- x 4- x 2 n -1 are in Arithmetic Progression- then find the value of - x 2 n -1- x 1 - x 2 n -1- x 1- x 2 n - x 2 - x 2 n - x 2- - - - - x n -2- x n - x n -2-x n -A- n-1B- nx1-x2 n-x1-xn-1C- nn-1 - 2D- n-1x2-x1E- -nn-1 - 2- -x2-x1 - xn-1-

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Progressions

If x 1, x 2, ...

Question

If x₁,x₂,x₃,x₄….x_2n+1are in Arithmetic Progression, then find the value of [(x_2n+1–x₁)/ (x_2n+1+x₁)] + [(x_2n–x₂)/ (x_2n–x₂)]………….. [(x_n+2–x_n)/ (x_n+2–x_n)]

n-1

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n(n+1)/2

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[n(n+1)/2]/[x₂-(x₁/x_n)+1]

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(n+1)(x₂-x₁)

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Solution

The correct option is D [n(n+1)/2]/[x₂-(x₁/x_n)+1]
Assumption assume an AP 1,2,3 substituting in the equation, we get the value as ½ at n=1 look in the answer options and eliminate those options, where you do not get ½ answer is option (d)

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Similar questions

If $x_{1}, x_{2}, x_{3} \dots x_{n}$ are roots of $x^{n} + a x + b = 0$ , then the value of $(x_{1} - x_{2}) (x_{1} - x_{3}) (x_{1} - x_{4}) \dots (x_{1} - x_{n})$ =

Q. If

x_{1}, x_{2}, . . . . x_{n}

are

n

non-zero real numbers such that

(x_{1}^{2} {+ x}_{2}^{2} + x_{3}^{2} + . . . . . x_{n + 1}^{2}) (x_{2}^{2} + x_{3}^{2} + x_{4}^{2} + . . . . x_{n}^{2}) \leq {(x_{1} x_{2} + x_{2} x_{3} + . . . . x_{n - 1} x_{n})}^{2}

then prove that

x_{1}, x_{2}, . x_{n}

are in

G . P .

lim x \to 1 \frac{(1 - x) (1 - x^{2}) . . . (1 - x^{2 n})}{{(1 - x) (1 - x^{2}) . . . (1 - x^{n})}^{2}}, n \in N

, equals

Q. If

x_{1} x_{2} x_{3} . . . . x_{n} = 1 (x_{1} > 0, i = 1, 2, . . . . . n),

prove that

x_{1} + x_{2} + . . . . . x_{n} \geq n (n \geq 2)

Q. If

x_{1}, x_{2}, x_{3}, . . . . . x_{n}

are the roots of

x^{n} + a x + b = 0

, then the value of

(x_{1} - x_{2}) (x_{1} - x_{3}) (x_{1} - x_{4}) . . . . . (x_{1} - x_{n})

, is:

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If x1,x2,x3,x4….x2n+1 are in Arithmetic Progression, then find the value of [(x2n+1 –x1)/ (x2n+1 +x1)] + [(x2n –x2)/ (x2n –x2)]………….. [(xn+2 –xn)/ (xn+2 –xn)]

The correct option is D [n(n+1)/2]/[x2-(x1/xn)+1]Assumption assume an AP 1,2,3 substituting in the equation, we get the value as ½ at n=1 look in the answer options and eliminate those options, where you do not get ½ answer is option (d)

If x₁,x₂,x₃,x₄….x_2n+1are in Arithmetic Progression, then find the value of [(x_2n+1–x₁)/ (x_2n+1+x₁)] + [(x_2n–x₂)/ (x_2n–x₂)]………….. [(x_n+2–x_n)/ (x_n+2–x_n)]

The correct option is D [n(n+1)/2]/[x₂-(x₁/x_n)+1]
Assumption assume an AP 1,2,3 substituting in the equation, we get the value as ½ at n=1 look in the answer options and eliminate those options, where you do not get ½ answer is option (d)