Question

F(1)= 8 1/2; f(n)= f( n-1) - 1/2; 5 1/2. Find the position of the given term

Answer 1

7th position

Step-by-step explanation:

The first term is f(1) = 8 1/2

So, the second term is:

f(n) = f(n-1) - 1/2

f(2) = f(2-1) - 1/2

f(2) = f(1) - 1/2

f(2) = 8 1/2 - 1/2

f(2) = 8

Then, we can calculate the next terms until we get 5 1/2 as:

`\begin{gathered} f(3)=f(2)-(1)/(2)=8-(1)/(2)=7(1)/(2) \\ f(4)=f(3)-(1)/(2)=7(1)/(2)-(1)/(2)=7 \\ f(5)=f(4)-(1)/(2)=7-(1)/(2)=6(1)/(2) \\ f(6)=f(5)-(1)/(2)=6(1)/(2)-(1)/(2)=6 \\ f(7)=f(6)-(1)/(2)=6-(1)/(2)=5(1)/(2) \end{gathered}`

So, f(7) is equal to 5 1/2. It means that the position of the term is the 7th position.