Discussion
The third term of an H.P. is 1/7 and the fifth term is 1/11. What is the first term?
Answer: A
The corresponding A.P. has a 3rd term of 7 and a 5th term of 11. So, \(a+2d=7\) and \(a+4d=11\). Subtracting the equations gives \(2d=4\), so \(d=2\). Substituting back, \(a+2(2)=7 \Rightarrow a+4=7 \Rightarrow a=3\). The first term of the A.P. is 3. The first term of the H.P. is the reciprocal, 1/3.
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