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Question

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


A

rmn

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B

mnr+1

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C

mnr

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D

mnr1

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Solution

The correct option is C

mnr


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+(m1)d = 1n ......(i)

a+(n1)d = 1m ......(i)

Solving these, we get a = 1mn, d = 1mn

Now, rth term of corresponding A.P.

= a+(r1)d = 1mn+(r1)1mn = 1+r1mn = rmn

Therefore rth term of corresponding H.P. is mnr

Note : Students should remember this question as a fact.


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