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- nx1-x2 n-x1-xn-1B- -nn-1 - 2- -x2-x1 - xn-1-C- n-1x2-x1D- n-1

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Series

If x 1, x 2, ...

Question

If $x_{1}, x_{2}, x_{3}, x_{4} . . . . x_{2 n + 1}$ are in Arithmetic Progression, then find the value of $[\frac{(x_{2 n + 1} - x_{1})}{(x_{2 n + 1} + x_{1})}] + [\frac{(x_{2 n} - x_{2})}{(x_{2 n} + x_{2})}] . . . . . . . . . . . . . . . . . . . . [\frac{(x_{n + 2 - x_{n}})}{(x_{n + 2} + x_{n})}]$

n-1

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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 C [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 $\frac{1}{2}$ at n=1

Look at the answer options and eliminate those options, where you do not get $\frac{1}{2}$

Answer is option (c)

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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}

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:

Q. If

x_{n} > x_{n - 1} > . . . > x_{2} > x_{1} > 1

, then the value of

{log}_{x_{1}} {log}_{x_{2}} {log}_{x_{3}} . . . {log}_{x_{n}} x_{n}^{(x_{n - 1})^{.^{.^{. x_{1}}}}}

will be

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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 C [n(n+1)/2]/[x2-(x1/xn)+1]Assumption Assume an AP 1,2,3 Substituting in the equation, we get the value as 12 at n=1 Look at the answer options and eliminate those options, where you do not get 12 Answer is option (c)

If $x_{1}, x_{2}, x_{3}, x_{4} . . . . x_{2 n + 1}$ are in Arithmetic Progression, then find the value of $[\frac{(x_{2 n + 1} - x_{1})}{(x_{2 n + 1} + x_{1})}] + [\frac{(x_{2 n} - x_{2})}{(x_{2 n} + x_{2})}] . . . . . . . . . . . . . . . . . . . . [\frac{(x_{n + 2 - x_{n}})}{(x_{n + 2} + x_{n})}]$

The correct option is C [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 $\frac{1}{2}$ at n=1

Look at the answer options and eliminate those options, where you do not get $\frac{1}{2}$

Answer is option (c)