Question

Which number should be added to the number $13,15,19$ so that the resulting numbers be consecutive term of a H.P.

• A. 7
• B. 6
• C. -6
• D. -7

Answer 1

The correct option is D -7

Let $x$ be added to the number $13,15,19$.

So, that new numbers $x+13,x+15,x+19$

According to the question,

$x+15=\frac{2(x+13)(x+19)}{x+13+x+19}$

$x+15=\frac{2(x^2+13x+19x+247)}{2x+32}$

$2x^2+32x+30x+480=2x^2+64x+494$

$62x+480=64x+494$

$-2x=14$

$x=-7$

Hence, this is the answer.