Select correct option(s).

(B) a, b, c are in G.P.

(C) a, b, c are in H.P.

(D) a+b+c = bc

*Solution*

We have, $a + \frac{1}{{b + \frac{1}{c}}} = \frac{{115}}{{16}}$

$ \Rightarrow a + \frac{c}{{bc + 1}} = \frac{{115}}{{15 + 1}}$

$ \Rightarrow a + \frac{c}{{bc + 1}} = \frac{{115}}{{5 \times 3 + 1}}$

$ \Rightarrow a + \frac{c}{{bc + 1}} = \frac{{16 \times 7 + 3}}{{5 \times 3 + 1}}$

$ \Rightarrow a + \frac{c}{{bc + 1}} = 7 + \frac{3}{{5 \times 3 + 1}}$

$\therefore \{ a,b,c\} \equiv \{ 7,5,3\} $

Hence, (A) & (D).