Question

If 5th term and 11th term of a harmonic progression are $\frac{1}{45}$ and $\frac{1}{69}$ respectively, then 16th term is

• A. $\frac{1}{89}$
• B. $\frac{1}{85}$
• C. $\frac{1}{81}$
• D. $\frac{1}{77}$

Answer 1

Answer: (A)

Since, 5th and 11th terms of a harmonic progression are
$\frac{1}{45}$ and $\frac{1}{69}$ respectively,
therefore 5th and 11th terms of the corresponding AP are 45 and 69 respectively.
$\therefore$ $45=a(5-1)d$
$\Rightarrow$ $45=a+4d$ ...(i) and $69=a+10d$ ...(ii)
On solving Eqs. (i) and (ii), we get $a=29,d=4$
$\therefore$ $T_{16}=29+15\times 4=89$
$\therefore$ 16th term of harmonic progression $=\frac{1}{89}$