Discussion
If the 5th term of an H.P. is 7 and 7th term is 5, then the 12th term is:
Answer: C
The corresponding A.P. has 5th term 1/7 and 7th term 1/5. So, \(a+4d=1/7\) and \(a+6d=1/5\). Subtracting gives \(2d = 1/5 - 1/7 = (7-5)/35 = 2/35\), so \(d=1/35\). Substituting back: \(a+4/35=1/7 \Rightarrow a = 1/7 - 4/35 = (5-4)/35 = 1/35\). The 12th term of the A.P. is \(a_{12} = a+11d = 1/35 + 11/35 = 12/35\). The 12th term of the H.P. is the reciprocal, 35/12.
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