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