Q If A1, A2 are two AMs between two numbers a and b, then (2A1 - A2) ( 2Aâ€‹2 - Maths - Arithmetic Progressions

Question

Q If A1, A2 are two AMs between two numbers a
and b, then (2A1 - A2) (
2Aâ€‹2 - A1) is equal
to
(A) a + b (B) a b a   +   b (C) ab (D) a   + b a b

Amit Shukla · Accepted Answer

Dear Student,

If A1 and A2 are two AM's of a and b then,As we know,a, A1 ,A2 ,b are in A
PSo, b+3dNow,→Common difference d=b-a3→A1=a+d= a+(b-a)3=2a+b3and,→A2=a+2d= a+2b-a3= a+2b3now,→2A1-A22A2-A1= 22a+b3-a+2b32a+2b3-2a+b3=4a+2b-a-2b32a+4b-2a-b3=3a3×3b3=abSo, option C is the correct answer

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Q. If A1, A2 are two AMs between two numbers a and b, then (2A1 - A2) ( 2A​2 - A1) is equal to (A) a + b (B) a b a + b (C) ab (D) a + b a b

Q. If A₁, A₂ are two AMs between two numbers a and b, then (2A₁ - A₂) ( 2A₂ - A₁) is equal to
(A) a + b (B) $\frac{a b}{a + b}$ (C) ab (D) $\frac{a + b}{a b}$