The first, fourth and tenth terms of the arithmetic sequence is [tex]-6, -\frac{27}{5}[/tex] and [tex]-\frac{21}{5}[/tex]
Explanation:
The given rule for the arithmetic sequence is [tex]A(n)=-6+(n-1)(\frac{1}{5} )[/tex]
We need to determine the first, fourth and tenth terms of the sequence.
To find the first, fourth and tenth terms, let us substitute [tex]n=1,4,10[/tex] in the general rule for the arithmetic sequence.
To find the first term, substitute [tex]n=1[/tex] in [tex]A(n)=-6+(n-1)(\frac{1}{5} )[/tex] , we get,
[tex]A(1)=-6+(1-1)(\frac{1}{5} )[/tex]
[tex]A(1)=-6+(0)(\frac{1}{5} )[/tex]
[tex]A(1)=-6[/tex]
Thus, the first term of the arithmetic sequence is -6.
To find the fourth term, substitute [tex]n=4[/tex] in [tex]A(n)=-6+(n-1)(\frac{1}{5} )[/tex] , we get,
[tex]A(2)=-6+(4-1)(\frac{1}{5} )[/tex]
[tex]A(2)=-6+(3)(\frac{1}{5} )[/tex]
[tex]A(2)=\frac{-30+3}{5}[/tex]
[tex]A(2)=\frac{-27}{5}[/tex]
Thus, the fourth term of the arithmetic sequence is [tex]-\frac{27}{5}[/tex]
To find the tenth term, substitute [tex]n=10[/tex] in [tex]A(n)=-6+(n-1)(\frac{1}{5} )[/tex] , we get,
[tex]A(10)=-6+(10-1)(\frac{1}{5} )[/tex]
[tex]A(10)=-6+(9)(\frac{1}{5} )[/tex]
[tex]A(10)=-6+\frac{9}{5}[/tex]
[tex]A(10)=-\frac{21}{5}[/tex]
Thus, the tenth term of the arithmetic sequence is [tex]-\frac{21}{5}[/tex]
Hence, the first, fourth and tenth terms of the arithmetic sequence is [tex]-6, -\frac{27}{5}[/tex] and [tex]-\frac{21}{5}[/tex]
