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Question

Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is


A

0,5,10.

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B

10,5,0.

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C

Both a and b

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D

None of these.

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Solution

The correct option is C

Both a and b


Since the three terms are in AP,
we can take the terms as a-d, a, a+d.
Sum of these terms= a - d + a +a + d = 3a

We have, 3a = 15

a = 5.
Also given that their product is 0.
(ad)a(a+d)=a(a2d2)=0
Since we already have a=5, a2d2=0

a2=d2
a=±d or d=±a
d=5,5
For d=5, the sequence is 0,5,10.
For d=-5, the sequence is 10,5,0


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