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  4. If pth term of an AP is q, and its qth term is p, then what is the common difference ?

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Q. If $p^{th}$ term of an AP is q, and its $q^{th}$ term is p, then what is the common difference ?

Sequences and Series

Solution:

Let first term and common difference of an AP are a and d respectively.
Its $p^th$ term = a + (p - 1) d = q ...(i)
and $q^{th}$ term = a + (q - 1) d = p ...(ii)
Solving Eqs. (i) and (ii), we find a = p + q -1, d = -1