We have been given the arithmetic sequence 4/5 , 29/30, 17/15 , 13/10
Let a be the first term and d be the common difference of the arithmetic sequence.
So let us first find the a and d
[tex]a=\frac{4}{5} \\\\d=\frac{29}{30} -\frac{4}{5} = \frac{1}{6}[/tex]
We know the nth term of an arithmetic sequence is given by
[tex]a_n=a+(n-1)d[/tex]
On substituting the known values, we get
[tex]a_n=\frac{4}{5} +(n-1) \frac{1}{6}[/tex]
On distributing 1/6 over the parenthesis, we get
[tex]\frac{n}{6}-\frac{1}{6}+\frac{4}{5}[/tex]
[tex]a_n=\frac{n}{6} +\frac{19}{30}[/tex]
[tex]a_n=\frac{5n+19}{30}[/tex]
Therefore, the explicit formula is given by
[tex]a_n=f(n)=\frac{5n+19}{30}[/tex]
