“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 (*n*th term), Meaning of Series

NCERT Exercise 9.1 |

Write the first five terms of each of the sequences in Exercises 1 to 6 whose n^{th} 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 *n*^{th} 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.