Answer:
Explicit formula is [tex]\frac{4}{5}+(n-1)(\frac{1}{6})[/tex]
Step-by-step explanation:
The given arithmetic sequence is 4/5, 29/30, 17/25, 13/10
The explicit formula of this sequence will be in the form of [tex]f{n}=A_{1}+d(n-1)[/tex]
Where [tex]f{n}[/tex]= nth term of the sequence
[tex]A_{1}[/tex]= first term of the sequence
n = number of terms
and d = Second term - first term
[tex]d=\frac{29}{30}-\frac{4}{5} =\frac{5}{30} =\frac{1}{6}[/tex]
Now we put the values in the explicit formula
[tex]f(n)=\frac{4}{5}+(n-1)(\frac{1}{6})[/tex]
Therefore the explicit formula of this arithmetic sequence is f(n)=[tex]\frac{4}{5}+(n-1)(\frac{1}{6})[/tex]
