Given:-
[tex]5,3,\frac{9}{5},\frac{27}{25},\ldots[/tex]
To find:-
Which function suits the sequence.
Considor the function,
[tex]f(n)=f(n-1)(\frac{3}{5}),f(1)=5[/tex]
When n = 2. we get,
[tex]\begin{gathered} f(2)=f(2-1)\times\frac{3}{5} \\ f(2)=f(1)\times\frac{3}{5} \\ f(2)=5\times\frac{3}{5} \\ f(2)=3 \end{gathered}[/tex]
So the second term is 3.
When n = 3. we get,
[tex]\begin{gathered} f(3)=f(3-1)\times\frac{3}{5} \\ f(3)=f(2)\times\frac{3}{5} \\ f(3)=3\times\frac{3}{5} \\ f(3)=\frac{9}{5} \end{gathered}[/tex]
So the third term is 9/5.
When n = 4. we get,
[tex]\begin{gathered} f(4)=f(4-1)\times\frac{3}{5} \\ f(4)=f(3)\times\frac{3}{5} \\ f(4)=\frac{9}{5}\times\frac{3}{5} \\ f(4)=\frac{27}{25} \end{gathered}[/tex]
So the fourth term is 27/25.
So this is the function which suits for the given sequence.
