$\text{ The }{5}^{\text{th }}\text{ and }{11}^{\text{th }}\text{ terms of an H.P are }\frac{1}{45}\text{ and }\frac{1}{69}\text{ respectively, then find 16th term}$

The 5^th and 11^th terms of the corresponding A.P. are 45

and 69 respectively. Let a be the first term and d be the common difference

of the  corresponding A.P then, 5^th term =a+4d=45…. (i)  and 

11^th term = a+10d=69….. (ii) 

Solving   equations   (i) and (ii), we get a=29, d=4  the 16^th term of  the A.P=$a+15d=29+15\left(4\right)=89$

Hence, the 16^th term  of the H.P = $\frac{1}{89}$