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
• D. None of these.

Answer 1

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

$\therefore$ a = 5.
Also given that their product is 0.
$\Rightarrow$$(a-d)a(a+d)=a(a^2-d^2)=0$
Since we already have $a=5$, $a^2-d^2=0$

$\Rightarrow$ $a^2=d^2$
$\therefore$$a=\pm d$ or $d=\pm a$
$\Rightarrow$$d=5,-5$
For d=5, the sequence is 0,5,10.
For d=-5, the sequence is 10,5,0