Question

x is one of the four harmonic means inserted between 2/3 and 2/13. The value/s of x can be:

• A. $\frac{2}{5}$
• B. $\frac{2}{11}$
• C. $\frac{2}{13}$
• D. $\frac{2}{15}$

Answer 1

Answer: (A), (B)

The correct options are
A $\frac{2}{5}$
B $\frac{2}{11}$

Let d be the common difference of the corresponding A.P. So,
$d=\frac{\frac{13}{2}-\frac{3}{2}}{5}=1\frac{1}{H_1}=\frac{3}{2}+1=\frac{5}{2}\Rightarrow H_1=\frac{2}{5}\frac{1}{H_2}=\frac{3}{2}+2=\frac{7}{2}\Rightarrow H_2=\frac{2}{7}\frac{1}{H_3}=\frac{3}{2}+3=\frac{9}{2}\Rightarrow H_3=\frac{2}{9}\frac{1}{H_4}=\frac{3}{2}+4=\frac{11}{2}\Rightarrow H_4=\frac{2}{11}$