“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.