Answer:
The first term is [tex]A(1)=5[/tex]
The fourth term is [tex]A(4)=\frac{11}{2}[/tex].
The tenth term is [tex]A(10)=\frac{13}{2}[/tex]
Step-by-step explanation:
Given : Arithmetic sequence [tex]A(n)=5+(n-1)( \frac{1}{6} )[/tex]
To find : The first, fourth, and tenth terms of the arithmetic sequence described by the given rule?
Solution :
Arithmetic sequence [tex]A(n)=5+(n-1)(\frac{1}{6})[/tex]
Substitute, n=1,4,10 to find the given terms
Put n=1,
[tex]A(1)=5+(1-1)(\frac{1}{6})[/tex]
[tex]A(1)=5+(0)(\frac{1}{6})[/tex]
[tex]A(1)=5[/tex]
The first term is [tex]A(1)=5[/tex]
Put n=4,
[tex]A(4)=5+(4-1)(\frac{1}{6})[/tex]
[tex]A(4)=5+(3)(\frac{1}{6})[/tex]
[tex]A(4)=5+\frac{1}{2}[/tex]
[tex]A(4)=\frac{11}{2}[/tex]
The fourth term is [tex]A(4)=\frac{11}{2}[/tex].
Put n=10,
[tex]A(10)=5+(10-1)(\frac{1}{6})[/tex]
[tex]A(10)=5+(9)(\frac{1}{6})[/tex]
[tex]A(10)=5+\frac{3}{2}[/tex]
[tex]A(10)=\frac{13}{2}[/tex]
The tenth term is [tex]A(10)=\frac{13}{2}[/tex]
