Question

solve this ques pls

Answer 1

Spq = 1/2 ( pq + 1)
step - by - step explanation
Tp = a + ( p -1 ) d = 1/q ------(i)
Tq = a + ( q -1 ) d = 1/p ------(ii)

To prove :-
Spq = 1/2 (pq + 1 )
solve eq (i) and (ii)
a + (q-1)d - a + (p-1)d = 1/p - 1/q
d ( q -1 -p + 1 ) = q-p/pq
here -1 and 1 gets cancelled out
d (q-p ) = q-p / pq
therefore , q-p gets cancelled out ...
d = 1/ pq -------(iii)
now ,substitute eq (iii) in eq (i)
a + (p-1) d = 1/q
a + p-1/ pq = 1/q
a + p/pq -1/ pq = 1/q
a + 1/q -1/pq = 1/q
take 1/q to other side ....
a - 1/pq = 1/q - 1/q
a - 1/pq = 0
a = 1/ pq ------(iv)
now ,to find Spq ....
Sn = n/2 + (2a + (n-1)d )
Spq = pq /2 + ( 2 × 1/pq + (pq -1 ) × 1/pq
Spq = pq /2 + (2 / pq + ( pq -1 /pq )
taking 1/pq common ...
Spq = pq / 2 × 1/ pq ( 2 + pq -1 )
Spq = pq / 2pq ( 1+ pq )
Spq = 1/2 ( 1 + pq )

hope this will help uh ....
nd plz mark as brainliest .....