Question

Drag each tile to the correct box. Not all tiles will be used.Consider the recursively defined function below. Create the first five terms of the sequence defined by the given function.

Answer 1

Given:

$\begin{gathered} f(1)=10 \\ f(n)=2.2\text{ .f\lparen n-1\rparen, for n=2,3,4......} \end{gathered}$

Required:

Create the first five terms of the sequence defined by the given function.

Explanation:

The first term of the sequence f(1) = 10

Second term

$\begin{gathered} f(2)=2.2\text{ f\lparen2-1\rparen} \\ f(2)\text{ = 2.2 f\lparen1\rparen} \\ f(2)=2.2(10) \\ f(2)=22 \end{gathered}$

The second term is f(2) = 22

Third term

$\begin{gathered} f(3)=2.2\text{ f\lparen3-1\rparen} \\ f(3)=2.2\text{ f\lparen2\rparen} \\ f(3)=2.2\text{ \lparen22\rparen} \\ f(3)=48.4 \end{gathered}$

The third term is f(3) = 48.4

Fourth term

$\begin{gathered} f(4)=2.2\text{ f\lparen4-1\rparen} \\ f(4)=2.2\text{ f\lparen3\rparen} \\ f(4)=2.2\text{ \lparen48.4\rparen} \\ f(4)=106.48 \end{gathered}$

The fourth term is f(4) = 106.48

Fifth term

$\begin{gathered} f(5)=2.2\text{ f\lparen5-1\rparen} \\ f(5)=2.2\text{ f\lparen4\rparen} \\ f(5)=2.2\text{ \lparen106.48\rparen} \\ f(5)=234.256 \end{gathered}$

The fifth term is f(5) = 234.256

Final Answer:

$\begin{gathered} f(1)=10 \\ f(2)=22 \\ f(3)=48.4 \\ f(4)=106.48 \\ f(5)=234.256 \end{gathered}$