“Practice Golden Rule Management In Everything You Do. Manage Others The Way You Would Like To Be Managed.”

# Lecture - 11 Chapter 9 Sequences & Series

MISCELLANEOUS EXERCISE |

**Question 1.** Show that the sum of \( (m+n)^{th} text{ and } (m-n)^{th}\) terms of an A.P. is equal to twice the *m*^{th} terms.

**Question 2.** If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

**Question 3.** Let the sum of *n*, 2*n*, 3*n* terms of an A.P. be \(S_1, S_2 \text{ and } S_3\), respectively, show that \(S_3=3(S_2-S_1)\)

**Question 4.** Find the sum of all numbers between 200 and 400 which are divisible by 7.

**Question 5.** Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

**Question 6.** Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

**Question 7.** If *f* is a function satisfying \( f (x +y) = f(x) f(y) \) for all *x*, *y* ∈ N such that\(f(1)=3\) and \( \sum_{x=1}^{n} f(x) = 120\), find the value of *n*.

**Question 8.** The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

**Question 9.** The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

**Question 10.** The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.