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Question

Suppose a,b,c are in A.P and a2,b2,c2 are in GP. If a < b < c and a+b+c = 32, then the value of a is


A

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B

-

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C

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D

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Solution

The correct option is B

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Let the number be

m - d, m, m + d

a b c

We will use the given three condition to find the value of m and d.

The first condition that they are in A.P is used to form the A.P.

There is one more condition (a<b<c)given,

Which we will use to eliminate any values of d and m at the end.

a+b+c = 32

m-d + m + m + d = 32

3m = 32

m = 12

(md)2,(m)2 , (m+d)2 are in GP

(m+d)2 (md)2 = (m)4

(m2d2)2 = (m)4

m2d2 = ¯¯¯¯+ m2

d2 = m2 ¯¯¯¯+ m2

d2 = 2m2 or d2 = 0

d ≠ 0 since a,b,c are different number (given a<b<c)

d = ¯¯¯¯+ 2m

= ¯¯¯¯+ 2 × 12

= ¯¯¯¯+ 12

Since a<b<c,d is positive

d = ¯¯¯¯+ 12

a = m - d

= 12 - 12


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