“Leadership Is The Ability To Get Extraordinary Achievement From Ordinary People”

 NCERT EXERCISE 9.2

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
terms.

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 $$(2m-1):(2n-1)$$.