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If the pth term of an A.P is1 /q and qth term is 1/q.Prove that the sum of first pq term of the A.P is (pq+1/2).

Posted by Ang Solanki 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 2 months ago

Given pth term = 1/q

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

aq + (pq - q)d = 1 --- (1)

Similarly,

ap + (pq - p)d = 1 --- (2)

From (1) and (2), we get

aq + (pq - q)d = ap + (pq - p)d

aq - ap = d[pq - p - pq + q]

a(q - p) = d(q - p)

Therefore, a = d

Equation (1) becomes,

dq + pqd - dq = 1

d = 1/pq

Hence a = 1/pq

Consider, Spq = (pq/2)[2a + (pq - 1)d]

= (pq/2)[2(1/pq) + (pq - 1)(1/pq)]

= (1/2)[2 + pq - 1]

= (1/2)[pq + 1]

1Thank You

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