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24. If the pth term of an A.P is - and the qh term is , show that the sum of pq term is24. İfthepthtermofanAPisqandthey®termísp,show thatthesumofpgtermis(21) |
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Answer» Given pth term = 1/qThat isap = a + (p - 1)d = 1/qaq + (pq - q)d = 1 --- (1)Similarly, we get ap + (pq - p)d = 1 --- (2)From (1) and (2), we getaq + (pq - q)d = ap + (pq - p)d aq - ap = d[pq - p - pq + q]a(q - p) = d(q - p)Therefore, a = dEquation (1) becomes,dq + pqd - dq = 1 d = 1/pqHence 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] thnx |
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