Question

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

Answer 1

pth term = a+(p-1)d= q
qth term= a+(q-1)d= p

eliminate

(p-1)-(q-1)d = q-p
(p-1-q+1)d = q-p
(p-q) d= q-p
d=-1

put value of d in eq 1
a+(p-1)-1=q
a-p+1 =q
a=q+p +1
a=2

(p+q)th term = a+(p+q-1) d
= 2+(1) -1
= 2-1=1

it was a try ...hope it helps

Answer 2

Let a be first term be a

And Common Difference be d

Therefore

$\bf\huge a_{p} = q , a_{q} = p$

a + (p - 1)d = q ……. (1)

a + (q - 1)d = p ……..(2)

Subtracting equations we get :-

(p - q)d = q - p

d = -1

Put the value of d in eq (1) :-

a + (p - 1)(-1) = q

a = (p + q - 1)

$\bf\huge a_{p + q} = a + (p + q - 1)d$

= (p + q - 1) + (p + q - 1)(-1)

= 0

Hence we get the (p + q)th term is Zero