SOLUTION:
Case: Sequence with factorial notation
A sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence.
Given:
[tex]a_n=\text{ }\frac{4}{n!}[/tex]Required: To find the first 4 terms
Method:
First term, n=1
[tex]\begin{gathered} a_{n}=\text{\frac{4}{n!}} \\ a_1=\frac{\text{4}}{1\text{!}} \\ a_1=\frac{\text{4}}{1} \\ a_1=\text{4} \end{gathered}[/tex]Second term, n= 2
[tex]\begin{gathered} a_2=\frac{\text{4}}{2!} \\ a_2=\frac{\text{4}}{2\times1} \\ a_2=\frac{\text{4}}{2} \\ a_2=2 \end{gathered}[/tex]Third term, n =3
[tex]\begin{gathered} a_3=\frac{\text{4}}{3!} \\ a_3=\frac{\text{4}}{3\times2\times1} \\ a_3=\frac{2}{3} \end{gathered}[/tex]Fourth term, n= 4
[tex]\begin{gathered} a_4=\frac{\text{4}}{4!} \\ a_4=\frac{\text{4}}{4\times3\times2\times1} \\ a_4=\frac{1}{6} \end{gathered}[/tex]Final answer:
First term, a= 4
Second term, a= 2
Third term, a= 2/3
Fourth term: a= 1/6
