Question

# If the mth term of a H.P. be n and nth be m, then the rth term will be

A

B

C

D

Solution

## The correct option is C Given Tm = n, Tn = m for H.P. therefore for the corresponding A.P. mth term = 1n, nth term  = 1m Let a and d be the first term and common difference of this A.P., then a+(m−1)d = 1n      ......(i) a+(n−1)d = 1m      ......(i) Solving these, we get a = 1mn, d = 1mn Now, rth term of corresponding A.P. = a+(r−1)d = 1mn+(r−1)1mn = 1+r−1mn = rmn Therefore rth term of corresponding H.P. is mnr Note : Students should remember this question as a fact.

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