In an AP, the pth term is q and (p + q)th term is 0. Show that its qth term is p.
Given: pth term is q and (p + q)th term is 0.
To prove: qth term is p.
pth term is given by
q = a + (p - 1) × d……equation1
(p + q)th term is given by
0 = a + (p + q - 1) × d
0 = a + (p - 1) × d + q × d
0 = q + q × d
d = - 1
Put in equation1 we get
a = q + p - 1
qth term is
⟹ q + p - 1 + (q - 1) × ( - 1)
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