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Question

If for an A.P. a1, a2, a3.........an, a1+a3+a5=12 and a1a2a3=8 then the value of a2+a4+a6 equals

A
12
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B
16
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C
18
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D
21
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Solution

The correct option is D 21
Solution -
A.P.a1,a2,....an
First element =a1
Common difference =d
a1+a1+2d+a1+4d=12
3a1+6d=12
a1+2d=4 ……(1)
a1a2a3=8
a1(a1+d)(a1+2d)=8
Put d1=42d from (1)
(42d)(4d)(4)=8
(4+2d)(4+d)=2
16+4d+8d+2d2=2
2d2+12d+18=0
d2+6d+9=0
(d+3)2=0
d=3
a1=4+6=2
a2=a1+d=1
a4=a1+3d=7
a6=a1+5d=13
a2+a4+a6=(1)+(7)+(13)=21
D is correct.

1058300_1114800_ans_29242221ce3448bea8291a7c6ddfc0f1.png

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