Question
If the pth term of an AP is q and its qth term is p then its mth term is:
Answer: Option B
:
B
pth term = a + (p – 1) d = q ... (i)q th term = a + (q – 1) d = p ... (ii)Subtracting (ii) from (i)(p – 1) d – (q – 1) d = q – p->pd – d – qd + d = q – p->d (p – q) = q – p-> d = -1a = q – (p – 1)d = q + (p – 1)So, mth term = q + p – 1 – (m – 1) = q + p – 1-m + 1 = p + q – mHence option (b)Alternatively, use assumptionLet the first term=2 and the 2nd term=1, therefore p=1 and q=2Let m=3Thus, 3rd term=0. Substitute the values of p,q and m in the answer options and look for 0. Only option (b) gives this value
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:
B
pth term = a + (p – 1) d = q ... (i)q th term = a + (q – 1) d = p ... (ii)Subtracting (ii) from (i)(p – 1) d – (q – 1) d = q – p->pd – d – qd + d = q – p->d (p – q) = q – p-> d = -1a = q – (p – 1)d = q + (p – 1)So, mth term = q + p – 1 – (m – 1) = q + p – 1-m + 1 = p + q – mHence option (b)Alternatively, use assumptionLet the first term=2 and the 2nd term=1, therefore p=1 and q=2Let m=3Thus, 3rd term=0. Substitute the values of p,q and m in the answer options and look for 0. Only option (b) gives this value
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