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# Lecture - 3 Chapter 9 Sequences & Series

NCERT EXERCISE 9.2 |

**Question 5.** In an A.P., if p^{th} term is \( \frac{1}{q}\) and q^{th} 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 k^{th} 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 5*n* + 4 : 9*n* + 6. Find the ratio of their 18^{th}

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 *m*^{th} and *n*^{th} terms is \((2m-1):(2n-1)\).