Question

If the p th term of an AP is q and q th term is p, prove that its n th term is (p+q-n)​

Answer 1

$\mathfrak{\huge{\green{\underline{\underline{ANSWER :}}}}}$

pth term = q

a+(p−1)d=q

qth term = p

a+(q−1)d=p

Solving these equations, we get,

d=−1

a=(p+q−1)

Thus,

nth term = a+(n−1)d = (p+q−1)+(n−1)×(−1) = (p+q−n)

Hope It Will Help.❤

Answer 2

Answer:

pth term = q

a+(p−1)d=q

qth term = p

a+(q−1)d=p

Solving these equations, we get,

d=−1

a=(p+q−1)

Thus,

nth term = a+(n−1)d = (p+q−1)+(n−1)×(−1) = (p+q−n)

Hope it will be helpful ✌️