Question

Write a recursive formula for the explicit formula.
A(n)=5+(n− 1)(-4)

Answer 1

`\large\begin{cases}a_1=5 \\a_n=a_((n-1))-4\end{cases}`

Explanation:

Recursive formula allows us to find the value of a specific term based on the previous term.

Explicit formula allows us to find the value of a specific term based on its position.

Given explicit formula:
`a(n)=5+(n-1)(-4)`

`\implies a(1)=5+(1-1)(-4)=5`

`\implies a(2)=5+(2-1)(-4)=1`

`\implies a(3)=5+(3-1)(-4)=-3`

`\implies a(4)=5+(4-1)(-4)=-7`

From inspection of the sequence, we can see that to get the next term, we need to subtract 4 from the previous term.

`5 \underset{-4}{\longrightarrow} 1 \underset{-4}{\longrightarrow} -3 \underset{-4}{\longrightarrow} -7`

Therefore, the recursive formula is:

`a_n=a_((n-1))-4`

For a recursive formula, we also need to give the value for
`a_1` .

Therefore, the final recursive formula for the explicit formula is:

`\large\begin{cases}a_1=5 \\a_n=a_((n-1))-4\end{cases}`