Nth term of HP


 
 
Concept Explanation
 

Nth Term of a HP

The nth term (T_n) of a harmonic progression is given by

                  T_n=frac{1}{a+(n-1)d}

Illustration 1. The third term of a HP is frac{1}{3}  and the sixth term is frac{1}{9}. Find the 1st term of the HP.

A. frac{1}{59}                   B. frac{1}{60}                C. frac{1}{68}                 D. frac{1}{61}

Answer: A

Solution The third and sixth terms of the HP's are

 frac{1}{3} and frac{1}{9} respectively.

Hence, for the corresponding AP, the third term is 3 and the six term is 9.

Hence,              a + 2d = 3              ...(i)

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