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If a, b, c are in AP, then which of the following is not an AP

Option: 1

\frac{1}{bc},\frac{1}{ac},\frac{1}{ab}


Option: 2

2a,2b,2c


Option: 3

c,b,a


Option: 4

a+d,b,c+d\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; (d\neq 0)


Answers (1)

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(A) As a,b,c are in A.P.

So, \frac{a}{abc},\frac{b}{abc},\frac{c}{abc}  are in AP       (dividing the same term gives a new AP)

\Rightarrow \frac{1}{bc},\frac{1}{ac},\frac{1}{ab} are in A.P.

 

(B)As a,b,c are in A.P.

So, 2a,2b,2c are in A.P      (multiplying the same term gives a new A.P)

(C) As a,b,c are in A.P.

So, c,b,a are in A.P       (Reverse of AP is also and AP)

Hence,  (D) is not an AP

Posted by

Pankaj Sanodiya

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