Question

the pth term of an AP is q and the qth term is p. find the ( p + q) th term

Answer 1

Hey

Here is your answer,

the given AP, let the first term be a and the common difference be d.
Then Tn = a + (n - 1)d ​
⇒ Tp = a + (p - 1)d = q ...(i)
​
⇒ Tq = a + (q - 1)d = p ...(ii)

On subtracting (i) from (ii), we get:
(q - p)d = (p - q)
⇒ d = -1
Putting d = -1 in (i), we get:
a = (p + q - 1)

Thus, a = (p + q - 1) and d = -1
Now, Tp+q = a + (p + q - 1)d
=​ (p + q - 1) + (p + q - 1)(-1)
= (p + q - 1) - (p + q - 1) = 0 ​

​Hence, the (p+q)th term is 0 (zero)

Hope it helps you!