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Question 5. In an A.P., if pth term is \( \frac{1}{q}\) and qth term is \( \frac{1}{p}\) prove that the sum of first pq terms is \(\frac{1}{2} (pq+1) \), where \(p ne q\).

Question 6. If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term.

Question 7. Find the sum to n terms of the A.P., whose kth term is \( 5k+1\).

Question 8. If the sum of n terms of an A.P. is \( (pn+qn^2)\), where p and q are constants, find the common difference.

Question 9. The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th

Question 10. If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

Question 11. Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that \( \frac{a}{p}(q-r)+\frac{b}{q}(r-p)+\frac{c}{r}(p-q) = 0\).

Question 12. The ratio of the sums of m and n terms of an A.P. is \( m^2:n^2\). Show that the ratio of mth and nth terms is \((2m-1):(2n-1)\).