EXERCISE 9.1

Find the terms ${\mathrm{a}}_{17} \mathrm{and} {\mathrm{a}}_{24}$ in the sequence whose $n^{th}$ term is $a_n=4n-3$

Find the term $a_7$ in the sequence whose $n^{th}$ term is $a_n=\frac{n^2}{2^n}$

Find the term ${\mathrm{a}}_9$ in the sequence whose $n^{th}$ term is ${\mathrm{a}}_{\mathrm{n}}={(-1)}^{\mathrm{n}-1}{\mathrm{n}}^3$

Find the term $a_{20}$ in the sequence whose $n^{th}$ term is ${\mathrm{a}}_{\mathrm{n}}=\frac{\mathrm{n}(\mathrm{n}-2)}{\mathrm{n}+3}$

Write the first five terms of the following sequence and obtain the corresponding series:
$a_1=3,a_n=3a_{n-1}+2$ for all $n>1$

Write the first five terms of the following sequence and obtain the corresponding series

$a_1=-1,a_n=\frac{a_{n-1}}{n},n\ge 2$

Write the first five terms of the following sequence and obtain the corresponding series

 $a_1=a_2=2,a_n=a_{n-1}-1,n>2$

The Fibonacci sequence is defined by $1=a_1=a_{2 }\mathrm{a}\mathrm{n}\mathrm{d} a_n=a_{n-1}+a_{n-2},n>2$
Find $\frac{a_{n+1}}{a_n}$ , for $n=1,2,3,4,5$