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Question

Suppose a, b, c are in A.P. and a2, b2, c2 are in G.P.. If a<b<c and a+ b+ c =32 , then 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 D

b=a1

a1d+a1+a1+d=32

c=a1+d

3a1=32

a1=12

b2a2=c2b2

b4=a2c2

(12)4=[(12+d)(12d)]2

[(12+d)(12d)]2=116

[14d2]=116

14d2=±14

d2=14+14=12 or d2=0 d=0 not applicable as a<b<c

d=±12

1212or12+12


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