plzZzzz solve this........
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Answer:
Spq = 1/2(pq+1)
Step-by-step explanation:
Tp = a + ( p - 1) d = 1/q ------- (1)
Tq = a + ( q - 1) d = 1/p ------(2)
To prove:
Spq = 1/2(pq+1)
Solve equation 1 and 2,
a + (p-1)d - [a + (q-1)d] = 1/p - 1/q
a + (q-1)d - a (p-1)d = q-p/pq
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 -----(3)
Now,
Substitute 3 in equation 1,
a + ( q - 1) d = 1/p
a + q - 1 / pq = 1/p
a + q/pq - 1/pq = 1/p
In q/pq , q gets cancelled out,
a + 1/p - 1/pq = 1/p
Take 1/p to other side,
a - 1/pq = 1/p - 1/p
a = 1/pq ----- (4)
Now ... to find Spq....
Sn = n/2[2a + (n-1)d]
Spq = pq /2 [ 2(1/pq) + ( pq - 1 ) 1/pq]
= pq / 2 [ 2/pq +( pq - 1)/pq]
Now, Take 1/pq common,
= pq / 2pq [ 2 + pq - 1]
= 1/2 [ 1 + pq ]
HENCE PROVED
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