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Question
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
Options
– p
p
p + q
p – q
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Solution
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is p.
Explanation:
Let a, d be the first term and common difference respectively.
Therefore, Tp = a + (p – 1)d = q ......(1)
Tp+ q = a + (p + q – 1)d = 0 .....(2)
Subtracting (1), from (2) we get qd = – q
Substituting in (1) we get
a = q – (p – 1)(–1) = q + p – 1
Now Tq = a + (q – 1)d = q + p – 1 + (q – 1)(–1)
= q + p – 1 – q + 1
= p
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