Q. . If x 1 ,x 2 , ………….x n are n non-zero real numbers such that (x 1 2 +x 2 2 + …..+x (n-1) 2 )(x 2 2 +x 3 2 + …..+x n 2 ) ≤ (x1,x2+ x2,x3+…….+ xn-1,xn) 2 , then x 1 ,x 2……………………. x n are in (a) A.P. (b) G.P. (c) H.P. (d) none of these

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Q. . If x 1 ,x 2 , &hellip;&hellip;&hellip;&hellip;.x n are n non-zero real numbers such that (x 1 2 +x 2 2 + &hellip;..+x (n-1) 2 )(x 2 2 +x 3 2 + &hellip;..+x n 2 ) &le; (x1,x2+ x2,x3+&hellip;&hellip;.+ xn-1,xn) 2 , then x 1 ,x 2&hellip;&hellip;&hellip;&hellip;&hellip;&hellip;&hellip;&hellip;. x n are in (a) A.P. (b) G.P. (c) H.P. (d) none of these

aman bansal · Answer

dear raghu,

the above question can be solved by expanding the terms and then converting it into a perfect square

for simplicity we can take n=3 and then conclude that it forms GP

hence answer is (B)

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Q. . If x 1 ,x 2 , ………….x n are n non-zero real numbers such that (x 1 2 +x 2 2 + …..+x (n-1) 2 )(x 2 2 +x 3 2 + …..+x n 2 ) ≤ (x1,x2+ x2,x3+…….+ xn-1,xn) 2 , then x 1 ,x 2……………………. x n are in (a) A.P. (b) G.P. (c) H.P. (d) none of these

Q. .    If x₁,x₂, ………….x_n are n non-zero real numbers such that

  (x₁²+x₂²+ …..+x_(n-1)²)(x₂²+x₃²+ …..+x_n²) ≤ (x1,x2+ x2,x3+…….+ xn-1,xn)²,

then x₁,x_{2…………………….} x_nare in

(a)   A.P.

(b)    G.P.

(c)    H.P.

(d)    none of these

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Q. . If x 1 ,x 2 , ………….x n are n non-zero real numbers such that (x 1 2 +x 2 2 + …..+x (n-1) 2 )(x 2 2 +x 3 2 + …..+x n 2 ) ≤ (x1,x2+ x2,x3+…….+ xn-1,xn) 2 , then x 1 ,x 2……………………. x n are in (a) A.P. (b) G.P. (c) H.P. (d) none of these

Q. . If x1,x2, ………….xn are n non-zero real numbers such that (x12+x22+ …..+x(n-1)2)(x22+x32+ …..+xn2) ≤ (x1,x2+ x2,x3+…….+ xn-1,xn)2, then x1,x2……………………. xn are in (a) A.P. (b) G.P. (c) H.P. (d) none of these

1 Answers

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Q. . If x₁,x₂, ………….x_n are n non-zero real numbers such that

(x₁²+x₂²+ …..+x_(n-1)²)(x₂²+x₃²+ …..+x_n²) ≤ (x1,x2+ x2,x3+…….+ xn-1,xn)²,

then x₁,x_{2…………………….} x_nare in

(a) A.P.

(b) G.P.

(c) H.P.

(d) none of these