Question

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

• A. 0,5,10.
• B. 10,5,0.
• C. Both a and b are correct.
• D. None of these.

Answer 1

The correct option is C

Both a and b are correct.

Given that three consecutive terms are in AP.
Let the terms be a - d, a, a + d.
Sum of these terms = 3a = 15.
So, a = 5.
Also their product ($a-d)\times a\times (a+a)=a\times (a^2-d^2)=0$
Now $a=5$, so $a^2-d^2=0$
Therefore $a=\pm d$
$d=5,-5$
For d=5, the sequence is 0,5,10.
For d=-5, the terms are 10,5,0