Lecture 11 Chapter 9 Sequences and Series

“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 mth 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, 2n, 3n 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 thatf(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.