## Lecture 1 Sequences and Series Class 11

“There Are No Limits To What You Can Accomplish, Except The Limits You Place On Your Own Thinking.” – Brian Tracy

# Lecture - 1 Chapter 9 Sequences & Series

Meaning of Sequences, Meaning of General Term (nth term), Meaning of Series

 NCERT Exercise 9.1

Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are:

Question 1. $$a_n = n(n+2)$$
Question 2. $$a_n = \frac{n}{n+1}$$
Question 3. $$a_n=2^n$$
Question 4. $$a_n=\frac{2n-3}{6}$$
Question 5. $$a_n=(-1)^{n-1} 5^{n+1}$$
Question 6. $$a_n=n \frac{n^2+5}{4}$$

Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are:

Question 7. $$a_n=4n-3; a_{17}, a_{24}$$
Question 8. $$a_n=\frac{n^2}{a^n}; a_7$$
Question 9. $$a_n=(-1)^{n-1}n^3; a_9$$
Question 10. $$a_n=\frac{n(n-2)}{n+3}; a_{20}$$

Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:

Question 11. $$a_1=3, a_n=3a_{n-1}+2$$ for all n>1
Question 12. $$a_1=-1, a_n=\frac{a_{n-1}}{n}, n \ge 2$$
Question 13. $$a_1=a_2=2, a_n=a_{n-1}-1, n>2$$
Question 14. The Fibonacci sequence is defined by
$$1=a_1=a_2 \text{ and } a_n=a_{n-1}+a_{n-2}, n>2$$
Find $$\frac{a_{n+1}}{a_n}$$ for n=1, 2, 3, 4, 5.